TSTP Solution File: ALG384-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG384-1 : 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 : n027.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 04:30:13 EDT 2024
% Result : Unsatisfiable 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 496
% Syntax : Number of formulae : 797 ( 349 unt; 0 def)
% Number of atoms : 1515 ( 210 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1210 ( 492 ~; 463 |; 0 &)
% ( 255 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 300 ( 298 usr; 256 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 8 con; 0-3 aty)
% Number of variables : 625 ( 625 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2500,plain,
$false,
inference(avatar_sat_refutation,[],[f589,f594,f599,f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f654,f659,f664,f669,f674,f679,f684,f689,f694,f699,f704,f709,f714,f719,f724,f729,f734,f739,f744,f749,f754,f759,f764,f769,f774,f779,f784,f789,f794,f799,f804,f809,f814,f819,f824,f829,f834,f839,f844,f849,f854,f859,f864,f869,f874,f879,f884,f889,f894,f899,f904,f909,f914,f919,f924,f929,f934,f939,f944,f949,f954,f959,f964,f969,f974,f979,f983,f987,f992,f997,f1002,f1007,f1012,f1017,f1022,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1107,f1125,f1129,f1133,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1178,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1211,f1215,f1219,f1223,f1228,f1232,f1236,f1275,f1279,f1283,f1287,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1457,f1461,f1465,f1469,f1473,f1477,f1494,f1529,f1623,f1780,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f1850,f1854,f1858,f1862,f1866,f1870,f1874,f1878,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f2038,f2094,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2144,f2148,f2152,f2156,f2160,f2164,f2168,f2172,f2176,f2180,f2184,f2188,f2192,f2196,f2200,f2305,f2449,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2499]) ).
fof(f2499,plain,
( ~ spl0_67
| spl0_82
| ~ spl0_229
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2458,f2198,f2137,f989,f916]) ).
fof(f916,plain,
( spl0_67
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f989,plain,
( spl0_82
<=> v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f2137,plain,
( spl0_229
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2198,plain,
( spl0_244
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2458,plain,
( v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_229
| ~ spl0_244 ),
inference(trivial_inequality_removal,[],[f2455]) ).
fof(f2455,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| v_c____ = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_229
| ~ spl0_244 ),
inference(superposition,[],[f2199,f2139]) ).
fof(f2139,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex)
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2137]) ).
fof(f2199,plain,
( ! [X1,X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X4,X1)
| c_HOL_Ozero__class_Ozero(X1) = X4
| ~ class_RealVector_Oreal__normed__vector(X1) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2198]) ).
fof(f2498,plain,
spl0_255,
inference(avatar_split_clause,[],[f374,f2496]) ).
fof(f2496,plain,
( spl0_255
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f374,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse__class_Odivide(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Oinverse__class_Oinverse(X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f2494,plain,
spl0_254,
inference(avatar_split_clause,[],[f260,f2492]) ).
fof(f2492,plain,
( spl0_254
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f260,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f2490,plain,
spl0_253,
inference(avatar_split_clause,[],[f218,f2488]) ).
fof(f2488,plain,
( spl0_253
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f218,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
fof(f2486,plain,
spl0_252,
inference(avatar_split_clause,[],[f203,f2484]) ).
fof(f2484,plain,
( spl0_252
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X1)
| X4 = X5
| ~ c_lessequals(X4,X5,X1)
| c_HOL_Oord__class_Oless(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f203,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X1)
| X4 = X5
| ~ c_lessequals(X4,X5,X1)
| c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f2482,plain,
spl0_251,
inference(avatar_split_clause,[],[f201,f2480]) ).
fof(f2480,plain,
( spl0_251
<=> ! [X2,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f201,axiom,
! [X2,X3,X1] :
( ~ class_Orderings_Oorder(X1)
| X2 = X3
| ~ c_lessequals(X3,X2,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
fof(f2478,plain,
spl0_250,
inference(avatar_split_clause,[],[f162,f2476]) ).
fof(f2476,plain,
( spl0_250
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Oorder(X1)
| X4 = X5
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f162,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Oorder(X1)
| X4 = X5
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
fof(f2474,plain,
spl0_249,
inference(avatar_split_clause,[],[f153,f2472]) ).
fof(f2472,plain,
( spl0_249
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f153,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2470,plain,
spl0_248,
inference(avatar_split_clause,[],[f119,f2468]) ).
fof(f2468,plain,
( spl0_248
<=> ! [X4,X0,X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_OscaleR__class_OscaleR(X0,X4,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X0,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f119,axiom,
! [X0,X1,X4] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_OscaleR__class_OscaleR(X0,X4,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X0,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
fof(f2466,plain,
spl0_247,
inference(avatar_split_clause,[],[f102,f2464]) ).
fof(f2464,plain,
( spl0_247
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Ometric__space(X1)
| X4 = X5
| ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X5,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f102,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Ometric__space(X1)
| X4 = X5
| ~ c_lessequals(c_RealVector_Odist__class_Odist(X4,X5,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_0) ).
fof(f2462,plain,
spl0_246,
inference(avatar_split_clause,[],[f20,f2460]) ).
fof(f2460,plain,
( spl0_246
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f20,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f2449,plain,
spl0_245,
inference(avatar_split_clause,[],[f2,f2447]) ).
fof(f2447,plain,
( spl0_245
<=> ! [X2,X1,X3] :
( ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2,axiom,
! [X2,X3,X1] :
( ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
fof(f2305,plain,
( ~ spl0_67
| ~ spl0_133
| spl0_230 ),
inference(avatar_split_clause,[],[f2225,f2141,f1217,f916]) ).
fof(f1217,plain,
( spl0_133
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f2141,plain,
( spl0_230
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2225,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_133
| spl0_230 ),
inference(resolution,[],[f2143,f1218]) ).
fof(f1218,plain,
( ! [X1,X4] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f2143,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_230 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f2200,plain,
spl0_244,
inference(avatar_split_clause,[],[f492,f2198]) ).
fof(f492,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f2196,plain,
spl0_243,
inference(avatar_split_clause,[],[f437,f2194]) ).
fof(f2194,plain,
( spl0_243
<=> ! [X13,X2] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(X2,X13),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f437,axiom,
! [X2,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(X2,X13),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_realpow__pos__nth2_0) ).
fof(f2192,plain,
spl0_242,
inference(avatar_split_clause,[],[f425,f2190]) ).
fof(f2190,plain,
( spl0_242
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f425,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
fof(f2188,plain,
spl0_241,
inference(avatar_split_clause,[],[f418,f2186]) ).
fof(f2186,plain,
( spl0_241
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(X1) != c_RealVector_Oof__real(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f418,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(X1) != c_RealVector_Oof__real(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
fof(f2184,plain,
spl0_240,
inference(avatar_split_clause,[],[f384,f2182]) ).
fof(f2182,plain,
( spl0_240
<=> ! [X29,X23,X30] :
( ~ c_lessequals(X29,X30,tc_RealDef_Oreal)
| ~ c_lessequals(X30,X23,tc_RealDef_Oreal)
| c_lessequals(X29,X23,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f384,axiom,
! [X29,X23,X30] :
( ~ c_lessequals(X29,X30,tc_RealDef_Oreal)
| ~ c_lessequals(X30,X23,tc_RealDef_Oreal)
| c_lessequals(X29,X23,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f2180,plain,
spl0_239,
inference(avatar_split_clause,[],[f316,f2178]) ).
fof(f2178,plain,
( spl0_239
<=> ! [X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X23,X1) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Osgn__class_Osgn(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f316,axiom,
! [X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oabs__class_Oabs(X23,X1) = c_HOL_Otimes__class_Otimes(X23,c_HOL_Osgn__class_Osgn(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
fof(f2176,plain,
spl0_238,
inference(avatar_split_clause,[],[f295,f2174]) ).
fof(f2174,plain,
( spl0_238
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f295,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2172,plain,
spl0_237,
inference(avatar_split_clause,[],[f254,f2170]) ).
fof(f2170,plain,
( spl0_237
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oabs__if(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f254,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oabs__if(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2168,plain,
spl0_236,
inference(avatar_split_clause,[],[f238,f2166]) ).
fof(f2166,plain,
( spl0_236
<=> ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f238,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__mono_0) ).
fof(f2164,plain,
spl0_235,
inference(avatar_split_clause,[],[f237,f2162]) ).
fof(f2162,plain,
( spl0_235
<=> ! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f237,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__less__cancel_0) ).
fof(f2160,plain,
spl0_234,
inference(avatar_split_clause,[],[f226,f2158]) ).
fof(f2158,plain,
( spl0_234
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Ometric__space(X1)
| X4 = X5
| c_RealVector_Odist__class_Odist(X4,X5,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f226,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Ometric__space(X1)
| X4 = X5
| c_RealVector_Odist__class_Odist(X4,X5,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__eq__0__iff_0) ).
fof(f2156,plain,
spl0_233,
inference(avatar_split_clause,[],[f198,f2154]) ).
fof(f2154,plain,
( spl0_233
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f198,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2152,plain,
spl0_232,
inference(avatar_split_clause,[],[f165,f2150]) ).
fof(f2150,plain,
( spl0_232
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f165,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f2148,plain,
spl0_231,
inference(avatar_split_clause,[],[f160,f2146]) ).
fof(f2146,plain,
( spl0_231
<=> ! [X4,X5] :
( ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f160,axiom,
! [X4,X5] :
( ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_1) ).
fof(f2144,plain,
( spl0_229
| ~ spl0_230
| ~ spl0_191
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1937,f1830,f1620,f2141,f2137]) ).
fof(f1620,plain,
( spl0_191
<=> c_lessequals(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1830,plain,
( spl0_197
<=> ! [X9,X8] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_RealDef_Oreal)
| ~ c_lessequals(X9,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1937,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex)
| ~ spl0_191
| ~ spl0_197 ),
inference(resolution,[],[f1831,f1622]) ).
fof(f1622,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1620]) ).
fof(f1831,plain,
( ! [X8,X9] :
( ~ c_lessequals(X9,X8,tc_RealDef_Oreal)
| ~ c_lessequals(X8,X9,tc_RealDef_Oreal)
| X8 = X9 )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1830]) ).
fof(f2135,plain,
spl0_228,
inference(avatar_split_clause,[],[f159,f2133]) ).
fof(f2133,plain,
( spl0_228
<=> ! [X4,X5] :
( c_lessequals(X4,X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f159,axiom,
! [X4,X5] :
( c_lessequals(X4,X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_Transcendental_Oexp(X5,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__le__cancel__iff_0) ).
fof(f2131,plain,
spl0_227,
inference(avatar_split_clause,[],[f138,f2129]) ).
fof(f2129,plain,
( spl0_227
<=> ! [X13,X1,X14] :
( ~ class_Nat_Osemiring__char__0(X1)
| X13 = X14
| c_Nat_Osemiring__1__class_Oof__nat(X13,X1) != c_Nat_Osemiring__1__class_Oof__nat(X14,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f138,axiom,
! [X1,X14,X13] :
( ~ class_Nat_Osemiring__char__0(X1)
| X13 = X14
| c_Nat_Osemiring__1__class_Oof__nat(X13,X1) != c_Nat_Osemiring__1__class_Oof__nat(X14,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f2127,plain,
spl0_226,
inference(avatar_split_clause,[],[f137,f2125]) ).
fof(f2125,plain,
( spl0_226
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X1),c_HOL_Oabs__class_Oabs(X4,X1),X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f137,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X4,X1),c_HOL_Oabs__class_Oabs(X4,X1),X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
fof(f2123,plain,
spl0_225,
inference(avatar_split_clause,[],[f133,f2121]) ).
fof(f2121,plain,
( spl0_225
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| X4 = X5
| c_RealVector_Oof__real(X4,X1) != c_RealVector_Oof__real(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f133,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| X4 = X5
| c_RealVector_Oof__real(X4,X1) != c_RealVector_Oof__real(X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
fof(f2119,plain,
spl0_224,
inference(avatar_split_clause,[],[f131,f2117]) ).
fof(f2117,plain,
( spl0_224
<=> ! [X2,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f131,axiom,
! [X2,X3,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f2115,plain,
spl0_223,
inference(avatar_split_clause,[],[f112,f2113]) ).
fof(f2113,plain,
( spl0_223
<=> ! [X4,X5] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X5,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f112,axiom,
! [X4,X5] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X5,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
fof(f2111,plain,
spl0_222,
inference(avatar_split_clause,[],[f36,f2109]) ).
fof(f2109,plain,
( spl0_222
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = X4
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Osgn__class_Osgn(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f36,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = X4
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Osgn__class_Osgn(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
fof(f2107,plain,
spl0_221,
inference(avatar_split_clause,[],[f35,f2105]) ).
fof(f2105,plain,
( spl0_221
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Osgn__class_Osgn(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f35,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Osgn__class_Osgn(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
fof(f2103,plain,
spl0_220,
inference(avatar_split_clause,[],[f33,f2101]) ).
fof(f2101,plain,
( spl0_220
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f33,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).
fof(f2099,plain,
spl0_219,
inference(avatar_split_clause,[],[f4,f2097]) ).
fof(f2097,plain,
( spl0_219
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oinverse__class_Oinverse(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f4,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oinverse__class_Oinverse(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f2094,plain,
spl0_218,
inference(avatar_split_clause,[],[f3,f2092]) ).
fof(f2092,plain,
( spl0_218
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oabs__class_Oabs(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f3,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = X2
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oabs__class_Oabs(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2038,plain,
( ~ spl0_54
| spl0_217
| ~ spl0_185
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1842,f1778,f1463,f2036,f851]) ).
fof(f851,plain,
( spl0_54
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f2036,plain,
( spl0_217
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal__of__preal(X0),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1463,plain,
( spl0_185
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1778,plain,
( spl0_192
<=> ! [X0] : c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1842,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal__of__preal(X0),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ class_Orderings_Opreorder(tc_RealDef_Oreal) )
| ~ spl0_185
| ~ spl0_192 ),
inference(resolution,[],[f1779,f1464]) ).
fof(f1464,plain,
( ! [X1,X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f1779,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal)
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1778]) ).
fof(f1914,plain,
spl0_216,
inference(avatar_split_clause,[],[f578,f1912]) ).
fof(f1912,plain,
( spl0_216
<=> ! [X2,X1] :
( c_RealVector_Onorm__class_Onorm(X2,X1) = c_RealVector_Onorm__class_Onorm(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f578,plain,
! [X2,X1] :
( c_RealVector_Onorm__class_Onorm(X2,X1) = c_RealVector_Onorm__class_Onorm(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(forward_demodulation,[],[f243,f1]) ).
fof(f1,axiom,
! [X0] : c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__norm__def_0) ).
fof(f243,axiom,
! [X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X2,X1) = c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
fof(f1910,plain,
spl0_215,
inference(avatar_split_clause,[],[f576,f1908]) ).
fof(f1908,plain,
( spl0_215
<=> ! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X0,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f576,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X0,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(forward_demodulation,[],[f355,f1]) ).
fof(f355,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra__1(X1)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__of__real_0) ).
fof(f1906,plain,
spl0_214,
inference(avatar_split_clause,[],[f473,f1904]) ).
fof(f1904,plain,
( spl0_214
<=> ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f473,axiom,
! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__sgn_0) ).
fof(f1902,plain,
spl0_213,
inference(avatar_split_clause,[],[f462,f1900]) ).
fof(f1900,plain,
( spl0_213
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f462,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).
fof(f1898,plain,
spl0_212,
inference(avatar_split_clause,[],[f461,f1896]) ).
fof(f1896,plain,
( spl0_212
<=> ! [X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f461,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).
fof(f1894,plain,
spl0_211,
inference(avatar_split_clause,[],[f451,f1892]) ).
fof(f1892,plain,
( spl0_211
<=> ! [X11,X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(X11,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f451,axiom,
! [X11,X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(X11,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Opos__bounded_0) ).
fof(f1890,plain,
( spl0_210
| ~ spl0_107
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f1841,f1778,f1097,f1888]) ).
fof(f1888,plain,
( spl0_210
<=> ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1097,plain,
( spl0_107
<=> ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_lessequals(X4,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1841,plain,
( ! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal)
| ~ spl0_107
| ~ spl0_192 ),
inference(resolution,[],[f1779,f1098]) ).
fof(f1098,plain,
( ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_lessequals(X4,X5,tc_RealDef_Oreal) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1886,plain,
spl0_209,
inference(avatar_split_clause,[],[f441,f1884]) ).
fof(f1884,plain,
( spl0_209
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f441,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_1) ).
fof(f1882,plain,
spl0_208,
inference(avatar_split_clause,[],[f440,f1880]) ).
fof(f1880,plain,
( spl0_208
<=> ! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f440,axiom,
! [X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).
fof(f1878,plain,
spl0_207,
inference(avatar_split_clause,[],[f435,f1876]) ).
fof(f1876,plain,
( spl0_207
<=> ! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f435,axiom,
! [X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lemma__tan__total_0) ).
fof(f1874,plain,
spl0_206,
inference(avatar_split_clause,[],[f356,f1872]) ).
fof(f1872,plain,
( spl0_206
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f356,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f1870,plain,
spl0_205,
inference(avatar_split_clause,[],[f337,f1868]) ).
fof(f1868,plain,
( spl0_205
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Ometric__space(X1)
| c_RealVector_Odist__class_Odist(X4,X5,X1) = c_RealVector_Odist__class_Odist(X5,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f337,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Ometric__space(X1)
| c_RealVector_Odist__class_Odist(X4,X5,X1) = c_RealVector_Odist__class_Odist(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__commute_0) ).
fof(f1866,plain,
spl0_204,
inference(avatar_split_clause,[],[f319,f1864]) ).
fof(f1864,plain,
( spl0_204
<=> ! [X13,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X13,X1) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f319,axiom,
! [X1,X13] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Nat_Osemiring__1__class_Oof__nat(X13,X1) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nat_0) ).
fof(f1862,plain,
spl0_203,
inference(avatar_split_clause,[],[f315,f1860]) ).
fof(f1860,plain,
( spl0_203
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f315,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X2,X1) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
fof(f1858,plain,
spl0_202,
inference(avatar_split_clause,[],[f239,f1856]) ).
fof(f1856,plain,
( spl0_202
<=> ! [X4,X5] :
( X4 = X5
| ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f239,axiom,
! [X4,X5] :
( X4 = X5
| ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f1854,plain,
spl0_201,
inference(avatar_split_clause,[],[f231,f1852]) ).
fof(f1852,plain,
( spl0_201
<=> ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_Transcendental_Oln(X4),tc_RealDef_Oreal) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f231,axiom,
! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_Transcendental_Oln(X4),tc_RealDef_Oreal) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ln__iff_0) ).
fof(f1850,plain,
spl0_200,
inference(avatar_split_clause,[],[f230,f1848]) ).
fof(f1848,plain,
( spl0_200
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_Transcendental_Oln(X4),tc_RealDef_Oreal) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f230,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_Transcendental_Oln(X4),tc_RealDef_Oreal) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ln_0) ).
fof(f1840,plain,
spl0_199,
inference(avatar_split_clause,[],[f178,f1838]) ).
fof(f1838,plain,
( spl0_199
<=> ! [X5] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f178,axiom,
! [X5] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).
fof(f1836,plain,
spl0_198,
inference(avatar_split_clause,[],[f177,f1834]) ).
fof(f1834,plain,
( spl0_198
<=> ! [X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f177,axiom,
! [X5] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_1) ).
fof(f1832,plain,
spl0_197,
inference(avatar_split_clause,[],[f161,f1830]) ).
fof(f161,axiom,
! [X8,X9] :
( X8 = X9
| ~ c_lessequals(X8,X9,tc_RealDef_Oreal)
| ~ c_lessequals(X9,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f1828,plain,
spl0_196,
inference(avatar_split_clause,[],[f125,f1826]) ).
fof(f1826,plain,
( spl0_196
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f125,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X2,X1),X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f1824,plain,
spl0_195,
inference(avatar_split_clause,[],[f122,f1822]) ).
fof(f1822,plain,
( spl0_195
<=> ! [X2,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f122,axiom,
! [X2,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f1820,plain,
spl0_194,
inference(avatar_split_clause,[],[f109,f1818]) ).
fof(f1818,plain,
( spl0_194
<=> ! [X4] :
( c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f109,axiom,
! [X4] :
( c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).
fof(f1816,plain,
spl0_193,
inference(avatar_split_clause,[],[f108,f1814]) ).
fof(f1814,plain,
( spl0_193
<=> ! [X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f108,axiom,
! [X4] :
( ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_1) ).
fof(f1780,plain,
( spl0_192
| ~ spl0_161
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f1686,f1620,f1365,f1778]) ).
fof(f1365,plain,
( spl0_161
<=> ! [X4,X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,c_RealDef_Oreal__of__preal(X4),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1686,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal)
| ~ spl0_161
| ~ spl0_191 ),
inference(resolution,[],[f1622,f1366]) ).
fof(f1366,plain,
( ! [X4,X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,c_RealDef_Oreal__of__preal(X4),tc_RealDef_Oreal) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f1623,plain,
( ~ spl0_55
| spl0_191
| spl0_1
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f1566,f1357,f586,f1620,f856]) ).
fof(f856,plain,
( spl0_55
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f586,plain,
( spl0_1
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1357,plain,
( spl0_159
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X5,X4,X1)
| c_HOL_Oord__class_Oless(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1566,plain,
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| spl0_1
| ~ spl0_159 ),
inference(resolution,[],[f1358,f588]) ).
fof(f588,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| spl0_1 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1358,plain,
( ! [X1,X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,X1)
| c_lessequals(X5,X4,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f1529,plain,
( spl0_190
| ~ spl0_31
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1241,f1140,f736,f1526]) ).
fof(f1526,plain,
( spl0_190
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f736,plain,
( spl0_31
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1140,plain,
( spl0_114
<=> ! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1241,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_31
| ~ spl0_114 ),
inference(resolution,[],[f1141,f738]) ).
fof(f738,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f1141,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1494,plain,
( spl0_189
| ~ spl0_67
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1240,f1131,f916,f1491]) ).
fof(f1491,plain,
( spl0_189
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1131,plain,
( spl0_112
<=> ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1240,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_67
| ~ spl0_112 ),
inference(resolution,[],[f1132,f918]) ).
fof(f918,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f1132,plain,
( ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1477,plain,
spl0_188,
inference(avatar_split_clause,[],[f582,f1475]) ).
fof(f1475,plain,
( spl0_188
<=> ! [X0] :
( c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f582,plain,
! [X0] :
( c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f426,f1]) ).
fof(f426,axiom,
! [X0] :
( c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f1473,plain,
spl0_187,
inference(avatar_split_clause,[],[f581,f1471]) ).
fof(f1471,plain,
( spl0_187
<=> ! [X4,X0] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(X4,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f581,plain,
! [X0,X4] :
( ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X4,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(X4,X0,tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f130,f1]) ).
fof(f130,axiom,
! [X0,X4] :
( c_lessequals(X4,X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X4,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
fof(f1469,plain,
spl0_186,
inference(avatar_split_clause,[],[f491,f1467]) ).
fof(f1467,plain,
( spl0_186
<=> ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f491,axiom,
! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
fof(f1465,plain,
spl0_185,
inference(avatar_split_clause,[],[f478,f1463]) ).
fof(f478,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f1461,plain,
spl0_184,
inference(avatar_split_clause,[],[f477,f1459]) ).
fof(f1459,plain,
( spl0_184
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f477,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1457,plain,
( spl0_183
| ~ spl0_42
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1237,f1123,f791,f1454]) ).
fof(f1454,plain,
( spl0_183
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f791,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1123,plain,
( spl0_110
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1237,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_42
| ~ spl0_110 ),
inference(resolution,[],[f1124,f793]) ).
fof(f793,plain,
( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f1124,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f1452,plain,
spl0_182,
inference(avatar_split_clause,[],[f476,f1450]) ).
fof(f1450,plain,
( spl0_182
<=> ! [X2,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f476,axiom,
! [X2,X3,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1448,plain,
spl0_181,
inference(avatar_split_clause,[],[f474,f1446]) ).
fof(f1446,plain,
( spl0_181
<=> ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f474,axiom,
! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f1444,plain,
spl0_180,
inference(avatar_split_clause,[],[f459,f1442]) ).
fof(f1442,plain,
( spl0_180
<=> ! [X4,X1] :
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f459,axiom,
! [X1,X4] :
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_0) ).
fof(f1440,plain,
spl0_179,
inference(avatar_split_clause,[],[f454,f1438]) ).
fof(f1438,plain,
( spl0_179
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f454,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__not__eq__zero_0) ).
fof(f1436,plain,
spl0_178,
inference(avatar_split_clause,[],[f452,f1434]) ).
fof(f1434,plain,
( spl0_178
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X5,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f452,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X4,X5,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__not__less__zero_0) ).
fof(f1432,plain,
spl0_177,
inference(avatar_split_clause,[],[f446,f1430]) ).
fof(f1430,plain,
( spl0_177
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oln(X4),X4,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f446,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_Transcendental_Oln(X4),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__less__self_0) ).
fof(f1428,plain,
spl0_176,
inference(avatar_split_clause,[],[f434,f1426]) ).
fof(f1426,plain,
( spl0_176
<=> ! [X0,X1,X26] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X26,X0,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f434,axiom,
! [X0,X1,X26] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X26,X0,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Opos__bounded_0) ).
fof(f1424,plain,
~ spl0_175,
inference(avatar_split_clause,[],[f430,f1421]) ).
fof(f1421,plain,
( spl0_175
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f430,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
fof(f1419,plain,
spl0_174,
inference(avatar_split_clause,[],[f423,f1417]) ).
fof(f1417,plain,
( spl0_174
<=> ! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_RealDef_Oreal__of__preal(X4),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f423,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X5,c_RealDef_Oreal__of__preal(X4),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__all__real2_0) ).
fof(f1415,plain,
spl0_173,
inference(avatar_split_clause,[],[f422,f1413]) ).
fof(f1413,plain,
( spl0_173
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f422,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
fof(f1411,plain,
( spl0_172
| ~ spl0_102
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1115,f1097,f1077,f1409]) ).
fof(f1409,plain,
( spl0_172
<=> ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1077,plain,
( spl0_102
<=> ! [X0,X33] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X33,X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1115,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X0,X1),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_107 ),
inference(resolution,[],[f1098,f1078]) ).
fof(f1078,plain,
( ! [X0,X33] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X33,X0),tc_RealDef_Oreal)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1077]) ).
fof(f1407,plain,
spl0_171,
inference(avatar_split_clause,[],[f421,f1405]) ).
fof(f1405,plain,
( spl0_171
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f421,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).
fof(f1403,plain,
spl0_170,
inference(avatar_split_clause,[],[f394,f1401]) ).
fof(f1401,plain,
( spl0_170
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X4,X5,X1)
| c_lessequals(X5,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f394,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X4,X5,X1)
| c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1399,plain,
spl0_169,
inference(avatar_split_clause,[],[f350,f1397]) ).
fof(f1397,plain,
( spl0_169
<=> ! [X4,X5] :
( c_lessequals(X4,X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f350,axiom,
! [X4,X5] :
( c_lessequals(X4,X5,tc_RealDef_Oreal)
| ~ c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).
fof(f1395,plain,
spl0_168,
inference(avatar_split_clause,[],[f349,f1393]) ).
fof(f1393,plain,
( spl0_168
<=> ! [X4,X5] :
( ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f349,axiom,
! [X4,X5] :
( ~ c_lessequals(X4,X5,tc_RealDef_Oreal)
| c_lessequals(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).
fof(f1391,plain,
spl0_167,
inference(avatar_split_clause,[],[f329,f1389]) ).
fof(f1389,plain,
( spl0_167
<=> ! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f329,axiom,
! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1387,plain,
spl0_166,
inference(avatar_split_clause,[],[f298,f1385]) ).
fof(f1385,plain,
( spl0_166
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f298,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1383,plain,
spl0_165,
inference(avatar_split_clause,[],[f266,f1381]) ).
fof(f1381,plain,
( spl0_165
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f266,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f1379,plain,
spl0_164,
inference(avatar_split_clause,[],[f253,f1377]) ).
fof(f1377,plain,
( spl0_164
<=> ! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f253,axiom,
! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f1375,plain,
spl0_163,
inference(avatar_split_clause,[],[f241,f1373]) ).
fof(f1373,plain,
( spl0_163
<=> ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f241,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).
fof(f1371,plain,
spl0_162,
inference(avatar_split_clause,[],[f240,f1369]) ).
fof(f1369,plain,
( spl0_162
<=> ! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f240,axiom,
! [X4,X5] :
( c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(X4),c_NthRoot_Osqrt(X5),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).
fof(f1367,plain,
spl0_161,
inference(avatar_split_clause,[],[f229,f1365]) ).
fof(f229,axiom,
! [X4,X5] :
( ~ c_lessequals(X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X5,c_RealDef_Oreal__of__preal(X4),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__all__preal_0) ).
fof(f1363,plain,
spl0_160,
inference(avatar_split_clause,[],[f216,f1361]) ).
fof(f1361,plain,
( spl0_160
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f216,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1359,plain,
spl0_159,
inference(avatar_split_clause,[],[f210,f1357]) ).
fof(f210,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X5,X4,X1)
| c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f1355,plain,
spl0_158,
inference(avatar_split_clause,[],[f209,f1353]) ).
fof(f1353,plain,
( spl0_158
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f209,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1351,plain,
spl0_157,
inference(avatar_split_clause,[],[f196,f1349]) ).
fof(f1349,plain,
( spl0_157
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| c_lessequals(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f196,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| c_lessequals(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1347,plain,
spl0_156,
inference(avatar_split_clause,[],[f188,f1345]) ).
fof(f1345,plain,
( spl0_156
<=> ! [X4,X5,X1] :
( ~ class_RealVector_Ometric__space(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X5,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f188,axiom,
! [X1,X4,X5] :
( ~ class_RealVector_Ometric__space(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X4,X5,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__dist_0) ).
fof(f1343,plain,
spl0_155,
inference(avatar_split_clause,[],[f181,f1341]) ).
fof(f1341,plain,
( spl0_155
<=> ! [X4,X5] :
( X4 = X5
| c_Transcendental_Oexp(X4,tc_RealDef_Oreal) != c_Transcendental_Oexp(X5,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f181,axiom,
! [X4,X5] :
( X4 = X5
| c_Transcendental_Oexp(X4,tc_RealDef_Oreal) != c_Transcendental_Oexp(X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__inj__iff_0) ).
fof(f1339,plain,
spl0_154,
inference(avatar_split_clause,[],[f149,f1337]) ).
fof(f1337,plain,
( spl0_154
<=> ! [X4,X1] :
( ~ class_RealVector_Ometric__space(X1)
| c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f149,axiom,
! [X1,X4] :
( ~ class_RealVector_Ometric__space(X1)
| c_lessequals(c_RealVector_Odist__class_Odist(X4,X4,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_1) ).
fof(f1335,plain,
spl0_153,
inference(avatar_split_clause,[],[f146,f1333]) ).
fof(f1333,plain,
( spl0_153
<=> ! [X13,X14] :
( X13 = X14
| c_RealDef_Oreal(X13,tc_nat) != c_RealDef_Oreal(X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f146,axiom,
! [X14,X13] :
( X13 = X14
| c_RealDef_Oreal(X13,tc_nat) != c_RealDef_Oreal(X14,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__inject_0) ).
fof(f1331,plain,
spl0_152,
inference(avatar_split_clause,[],[f92,f1329]) ).
fof(f1329,plain,
( spl0_152
<=> ! [X4,X5,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| c_lessequals(X4,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f92,axiom,
! [X1,X4,X5] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1)
| c_lessequals(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1327,plain,
( spl0_151
| ~ spl0_93
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1113,f1097,f1041,f1325]) ).
fof(f1325,plain,
( spl0_151
<=> ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1041,plain,
( spl0_93
<=> ! [X27] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X27),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1113,plain,
( ! [X0] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X0),tc_RealDef_Oreal)
| ~ spl0_93
| ~ spl0_107 ),
inference(resolution,[],[f1098,f1042]) ).
fof(f1042,plain,
( ! [X27] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X27),tc_RealDef_Oreal)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1041]) ).
fof(f1323,plain,
spl0_150,
inference(avatar_split_clause,[],[f37,f1321]) ).
fof(f1321,plain,
( spl0_150
<=> ! [X4,X1] :
( ~ class_SEQ_Obanach(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_Transcendental_Oexp(X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f37,axiom,
! [X1,X4] :
( ~ class_SEQ_Obanach(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_Transcendental_Oexp(X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f1319,plain,
spl0_149,
inference(avatar_split_clause,[],[f34,f1317]) ).
fof(f1317,plain,
( spl0_149
<=> ! [X5,X1] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f34,axiom,
! [X1,X5] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f1315,plain,
spl0_148,
inference(avatar_split_clause,[],[f31,f1313]) ).
fof(f1313,plain,
( spl0_148
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f31,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1311,plain,
spl0_147,
inference(avatar_split_clause,[],[f30,f1309]) ).
fof(f1309,plain,
( spl0_147
<=> ! [X2,X1] :
( ~ class_RealVector_Oreal__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f30,axiom,
! [X2,X1] :
( ~ class_RealVector_Oreal__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f1307,plain,
spl0_146,
inference(avatar_split_clause,[],[f29,f1305]) ).
fof(f1305,plain,
( spl0_146
<=> ! [X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f29,axiom,
! [X2,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f1303,plain,
spl0_145,
inference(avatar_split_clause,[],[f19,f1301]) ).
fof(f1301,plain,
( spl0_145
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f19,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1299,plain,
spl0_144,
inference(avatar_split_clause,[],[f18,f1297]) ).
fof(f1297,plain,
( spl0_144
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f18,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1295,plain,
spl0_143,
inference(avatar_split_clause,[],[f16,f1293]) ).
fof(f1293,plain,
( spl0_143
<=> ! [X1,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f16,axiom,
! [X3,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f1291,plain,
spl0_142,
inference(avatar_split_clause,[],[f14,f1289]) ).
fof(f1289,plain,
( spl0_142
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f14,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f1287,plain,
spl0_141,
inference(avatar_split_clause,[],[f12,f1285]) ).
fof(f1285,plain,
( spl0_141
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f12,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1283,plain,
spl0_140,
inference(avatar_split_clause,[],[f11,f1281]) ).
fof(f1281,plain,
( spl0_140
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f11,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Omult__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1279,plain,
spl0_139,
inference(avatar_split_clause,[],[f10,f1277]) ).
fof(f1277,plain,
( spl0_139
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f10,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1275,plain,
spl0_138,
inference(avatar_split_clause,[],[f9,f1273]) ).
fof(f1273,plain,
( spl0_138
<=> ! [X2,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f9,axiom,
! [X2,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1236,plain,
spl0_137,
inference(avatar_split_clause,[],[f575,f1234]) ).
fof(f1234,plain,
( spl0_137
<=> ! [X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal)) = c_RealVector_Onorm__class_Onorm(X4,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f575,plain,
! [X4] : c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal)) = c_RealVector_Onorm__class_Onorm(X4,tc_RealDef_Oreal),
inference(forward_demodulation,[],[f376,f1]) ).
fof(f376,axiom,
! [X4] : c_HOL_Oabs__class_Oabs(X4,tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X4,X4,tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
fof(f1232,plain,
spl0_136,
inference(avatar_split_clause,[],[f493,f1230]) ).
fof(f1230,plain,
( spl0_136
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f493,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X4,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f1228,plain,
( spl0_135
| ~ spl0_88
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1117,f1097,f1019,f1225]) ).
fof(f1225,plain,
( spl0_135
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1019,plain,
( spl0_88
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1117,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_88
| ~ spl0_107 ),
inference(resolution,[],[f1098,f1021]) ).
fof(f1021,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1223,plain,
spl0_134,
inference(avatar_split_clause,[],[f484,f1221]) ).
fof(f1221,plain,
( spl0_134
<=> ! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f484,axiom,
! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1219,plain,
spl0_133,
inference(avatar_split_clause,[],[f472,f1217]) ).
fof(f472,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1215,plain,
spl0_132,
inference(avatar_split_clause,[],[f471,f1213]) ).
fof(f1213,plain,
( spl0_132
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f471,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_Opos__bounded_0) ).
fof(f1211,plain,
spl0_131,
inference(avatar_split_clause,[],[f466,f1209]) ).
fof(f1209,plain,
( spl0_131
<=> ! [X1,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X24,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f466,axiom,
! [X1,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X24,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).
fof(f1207,plain,
spl0_130,
inference(avatar_split_clause,[],[f448,f1205]) ).
fof(f1205,plain,
( spl0_130
<=> ! [X12,X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(X12,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f448,axiom,
! [X1,X12] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(X12,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Opos__bounded_0) ).
fof(f1203,plain,
spl0_129,
inference(avatar_split_clause,[],[f431,f1201]) ).
fof(f1201,plain,
( spl0_129
<=> ! [X5,X1] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(X5,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f431,axiom,
! [X1,X5] :
( ~ class_RealVector_Oreal__normed__field(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(X5,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Opos__bounded_0) ).
fof(f1199,plain,
spl0_128,
inference(avatar_split_clause,[],[f429,f1197]) ).
fof(f1197,plain,
( spl0_128
<=> ! [X5,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X5,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f429,axiom,
! [X1,X5] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X5,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).
fof(f1195,plain,
spl0_127,
inference(avatar_split_clause,[],[f427,f1193]) ).
fof(f1193,plain,
( spl0_127
<=> ! [X4,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f427,axiom,
! [X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_0) ).
fof(f1191,plain,
spl0_126,
inference(avatar_split_clause,[],[f419,f1189]) ).
fof(f1189,plain,
( spl0_126
<=> ! [X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f419,axiom,
! [X1] :
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
fof(f1187,plain,
spl0_125,
inference(avatar_split_clause,[],[f399,f1185]) ).
fof(f1185,plain,
( spl0_125
<=> ! [X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f399,axiom,
! [X1,X14] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X14,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f1183,plain,
( spl0_124
| ~ spl0_86
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1116,f1097,f1009,f1180]) ).
fof(f1180,plain,
( spl0_124
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1009,plain,
( spl0_86
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1116,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_107 ),
inference(resolution,[],[f1098,f1011]) ).
fof(f1011,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1178,plain,
spl0_123,
inference(avatar_split_clause,[],[f392,f1176]) ).
fof(f1176,plain,
( spl0_123
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f392,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1174,plain,
spl0_122,
inference(avatar_split_clause,[],[f367,f1172]) ).
fof(f1172,plain,
( spl0_122
<=> ! [X4] : c_Transcendental_Oexp(X4,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f367,axiom,
! [X4] : c_Transcendental_Oexp(X4,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__exp__cancel_0) ).
fof(f1170,plain,
spl0_121,
inference(avatar_split_clause,[],[f256,f1168]) ).
fof(f1168,plain,
( spl0_121
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f256,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1166,plain,
spl0_120,
inference(avatar_split_clause,[],[f225,f1164]) ).
fof(f1164,plain,
( spl0_120
<=> ! [X4,X1] :
( ~ class_RealVector_Ometric__space(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f225,axiom,
! [X1,X4] :
( ~ class_RealVector_Ometric__space(X1)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Odist__class_Odist(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__self_0) ).
fof(f1162,plain,
spl0_119,
inference(avatar_split_clause,[],[f221,f1160]) ).
fof(f1160,plain,
( spl0_119
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f221,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X4
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_NthRoot_Osqrt(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).
fof(f1158,plain,
spl0_118,
inference(avatar_split_clause,[],[f189,f1156]) ).
fof(f1156,plain,
( spl0_118
<=> ! [X4] : c_RealDef_Oreal(X4,tc_nat) = c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X4,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f189,axiom,
! [X4] : c_RealDef_Oreal(X4,tc_nat) = c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(X4,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__real__of__nat__cancel_0) ).
fof(f1154,plain,
spl0_117,
inference(avatar_split_clause,[],[f123,f1152]) ).
fof(f1152,plain,
( spl0_117
<=> ! [X9,X8] : c_HOL_Otimes__class_Otimes(X8,X9,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X9,X8,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f123,axiom,
! [X8,X9] : c_HOL_Otimes__class_Otimes(X8,X9,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X9,X8,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
fof(f1150,plain,
spl0_116,
inference(avatar_split_clause,[],[f100,f1148]) ).
fof(f1148,plain,
( spl0_116
<=> ! [X13,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f100,axiom,
! [X1,X13] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Nat_Osemiring__1__class_Oof__nat(X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
fof(f1146,plain,
spl0_115,
inference(avatar_split_clause,[],[f28,f1144]) ).
fof(f1144,plain,
( spl0_115
<=> ! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f28,axiom,
! [X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1142,plain,
spl0_114,
inference(avatar_split_clause,[],[f22,f1140]) ).
fof(f22,axiom,
! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1138,plain,
( spl0_113
| ~ spl0_85
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1114,f1097,f1004,f1135]) ).
fof(f1135,plain,
( spl0_113
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f1004,plain,
( spl0_85
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1114,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_85
| ~ spl0_107 ),
inference(resolution,[],[f1098,f1006]) ).
fof(f1006,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f1133,plain,
spl0_112,
inference(avatar_split_clause,[],[f8,f1131]) ).
fof(f8,axiom,
! [X1] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
fof(f1129,plain,
spl0_111,
inference(avatar_split_clause,[],[f7,f1127]) ).
fof(f1127,plain,
( spl0_111
<=> ! [X1] :
( ~ class_Ring__and__Field_Osgn__if(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f7,axiom,
! [X1] :
( ~ class_Ring__and__Field_Osgn__if(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
fof(f1125,plain,
spl0_110,
inference(avatar_split_clause,[],[f6,f1123]) ).
fof(f6,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
fof(f1107,plain,
spl0_109,
inference(avatar_split_clause,[],[f395,f1105]) ).
fof(f1105,plain,
( spl0_109
<=> ! [X9,X8] :
( c_lessequals(X8,X9,tc_RealDef_Oreal)
| c_lessequals(X9,X8,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f395,axiom,
! [X8,X9] :
( c_lessequals(X8,X9,tc_RealDef_Oreal)
| c_lessequals(X9,X8,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1103,plain,
spl0_108,
inference(avatar_split_clause,[],[f365,f1101]) ).
fof(f1101,plain,
( spl0_108
<=> ! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f365,axiom,
! [X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1099,plain,
spl0_107,
inference(avatar_split_clause,[],[f236,f1097]) ).
fof(f236,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X4,X5,tc_RealDef_Oreal)
| c_lessequals(X4,X5,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f1095,plain,
spl0_106,
inference(avatar_split_clause,[],[f180,f1093]) ).
fof(f1093,plain,
( spl0_106
<=> ! [X4,X5] :
( X4 = X5
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f180,axiom,
! [X4,X5] :
( X4 = X5
| c_NthRoot_Osqrt(X4) != c_NthRoot_Osqrt(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).
fof(f1091,plain,
spl0_105,
inference(avatar_split_clause,[],[f470,f1089]) ).
fof(f1089,plain,
( spl0_105
<=> ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f470,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__gt__zero_0) ).
fof(f1087,plain,
spl0_104,
inference(avatar_split_clause,[],[f460,f1085]) ).
fof(f1085,plain,
( spl0_104
<=> ! [X13] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X13,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f460,axiom,
! [X13] : ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(X13,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).
fof(f1083,plain,
spl0_103,
inference(avatar_split_clause,[],[f455,f1081]) ).
fof(f1081,plain,
( spl0_103
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f455,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__exp__less__zero_0) ).
fof(f1079,plain,
spl0_102,
inference(avatar_split_clause,[],[f444,f1077]) ).
fof(f444,axiom,
! [X0,X33] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X33,X0),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).
fof(f1075,plain,
spl0_101,
inference(avatar_split_clause,[],[f224,f1073]) ).
fof(f1073,plain,
( spl0_101
<=> ! [X13] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f224,axiom,
! [X13] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Oroot(X13,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__root__zero_0) ).
fof(f1071,plain,
spl0_100,
inference(avatar_split_clause,[],[f127,f1069]) ).
fof(f1069,plain,
( spl0_100
<=> ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f127,axiom,
! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(X4,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ge__zero_0) ).
fof(f1067,plain,
spl0_99,
inference(avatar_split_clause,[],[f120,f1065]) ).
fof(f1065,plain,
( spl0_99
<=> ! [X4] : ~ c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f120,axiom,
! [X4] : ~ c_lessequals(c_Transcendental_Oexp(X4,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__exp__le__zero_0) ).
fof(f1063,plain,
spl0_98,
inference(avatar_split_clause,[],[f113,f1061]) ).
fof(f1061,plain,
( spl0_98
<=> ! [X13] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X13,tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f113,axiom,
! [X13] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(X13,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_0) ).
fof(f1059,plain,
spl0_97,
inference(avatar_split_clause,[],[f1,f1057]) ).
fof(f1057,plain,
( spl0_97
<=> ! [X0] : c_RealVector_Onorm__class_Onorm(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1055,plain,
spl0_96,
inference(avatar_split_clause,[],[f483,f1053]) ).
fof(f1053,plain,
( spl0_96
<=> ! [X4,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f483,axiom,
! [X1,X4] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1051,plain,
spl0_95,
inference(avatar_split_clause,[],[f482,f1049]) ).
fof(f1049,plain,
( spl0_95
<=> ! [X4,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f482,axiom,
! [X1,X4] :
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1047,plain,
spl0_94,
inference(avatar_split_clause,[],[f480,f1045]) ).
fof(f1045,plain,
( spl0_94
<=> ! [X4,X1] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f480,axiom,
! [X1,X4] :
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1043,plain,
spl0_93,
inference(avatar_split_clause,[],[f433,f1041]) ).
fof(f433,axiom,
! [X27] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(X27),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__gt__zero__preal__Ex_1) ).
fof(f1039,plain,
spl0_92,
inference(avatar_split_clause,[],[f383,f1037]) ).
fof(f1037,plain,
( spl0_92
<=> ! [X4,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f383,axiom,
! [X1,X4] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1035,plain,
spl0_91,
inference(avatar_split_clause,[],[f382,f1033]) ).
fof(f1033,plain,
( spl0_91
<=> ! [X4,X1] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X4,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f382,axiom,
! [X1,X4] :
( ~ class_Orderings_Opreorder(X1)
| c_lessequals(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1031,plain,
spl0_90,
inference(avatar_split_clause,[],[f331,f1029]) ).
fof(f1029,plain,
( spl0_90
<=> ! [X25] : c_Transcendental_Oln(c_Transcendental_Oexp(X25,tc_RealDef_Oreal)) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f331,axiom,
! [X25] : c_Transcendental_Oln(c_Transcendental_Oexp(X25,tc_RealDef_Oreal)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__ln__eq_0) ).
fof(f1027,plain,
spl0_89,
inference(avatar_split_clause,[],[f223,f1024]) ).
fof(f1024,plain,
( spl0_89
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f223,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).
fof(f1022,plain,
spl0_88,
inference(avatar_split_clause,[],[f465,f1019]) ).
fof(f465,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Opos__bounded_0) ).
fof(f1017,plain,
~ spl0_87,
inference(avatar_split_clause,[],[f463,f1014]) ).
fof(f1014,plain,
( spl0_87
<=> c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f463,axiom,
~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).
fof(f1012,plain,
spl0_86,
inference(avatar_split_clause,[],[f453,f1009]) ).
fof(f453,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Opos__bounded_0) ).
fof(f1007,plain,
spl0_85,
inference(avatar_split_clause,[],[f428,f1004]) ).
fof(f428,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Opos__bounded_0) ).
fof(f1002,plain,
spl0_84,
inference(avatar_split_clause,[],[f424,f999]) ).
fof(f999,plain,
( spl0_84
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f424,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).
fof(f997,plain,
spl0_83,
inference(avatar_split_clause,[],[f381,f994]) ).
fof(f994,plain,
( spl0_83
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f381,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).
fof(f992,plain,
~ spl0_82,
inference(avatar_split_clause,[],[f496,f989]) ).
fof(f496,axiom,
v_c____ != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f987,plain,
spl0_81,
inference(avatar_split_clause,[],[f481,f985]) ).
fof(f985,plain,
( spl0_81
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f481,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f983,plain,
spl0_80,
inference(avatar_split_clause,[],[f385,f981]) ).
fof(f981,plain,
( spl0_80
<=> ! [X9] : c_lessequals(X9,X9,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f385,axiom,
! [X9] : c_lessequals(X9,X9,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f979,plain,
~ spl0_79,
inference(avatar_split_clause,[],[f222,f976]) ).
fof(f976,plain,
( spl0_79
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Transcendental_Opi ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f222,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Transcendental_Opi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).
fof(f974,plain,
spl0_78,
inference(avatar_split_clause,[],[f574,f971]) ).
fof(f971,plain,
( spl0_78
<=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f574,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
fof(f969,plain,
spl0_77,
inference(avatar_split_clause,[],[f573,f966]) ).
fof(f966,plain,
( spl0_77
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f573,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f964,plain,
spl0_76,
inference(avatar_split_clause,[],[f572,f961]) ).
fof(f961,plain,
( spl0_76
<=> class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f572,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
fof(f959,plain,
spl0_75,
inference(avatar_split_clause,[],[f571,f956]) ).
fof(f956,plain,
( spl0_75
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f571,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f954,plain,
spl0_74,
inference(avatar_split_clause,[],[f570,f951]) ).
fof(f951,plain,
( spl0_74
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f570,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
fof(f949,plain,
spl0_73,
inference(avatar_split_clause,[],[f569,f946]) ).
fof(f946,plain,
( spl0_73
<=> class_RealVector_Ometric__space(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f569,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
fof(f944,plain,
spl0_72,
inference(avatar_split_clause,[],[f568,f941]) ).
fof(f941,plain,
( spl0_72
<=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f568,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
fof(f939,plain,
spl0_71,
inference(avatar_split_clause,[],[f567,f936]) ).
fof(f936,plain,
( spl0_71
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f567,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(f934,plain,
spl0_70,
inference(avatar_split_clause,[],[f566,f931]) ).
fof(f931,plain,
( spl0_70
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f566,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(f929,plain,
spl0_69,
inference(avatar_split_clause,[],[f565,f926]) ).
fof(f926,plain,
( spl0_69
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f565,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f924,plain,
spl0_68,
inference(avatar_split_clause,[],[f564,f921]) ).
fof(f921,plain,
( spl0_68
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f564,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f919,plain,
spl0_67,
inference(avatar_split_clause,[],[f563,f916]) ).
fof(f563,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f914,plain,
spl0_66,
inference(avatar_split_clause,[],[f562,f911]) ).
fof(f911,plain,
( spl0_66
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f562,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f909,plain,
spl0_65,
inference(avatar_split_clause,[],[f561,f906]) ).
fof(f906,plain,
( spl0_65
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f561,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f904,plain,
spl0_64,
inference(avatar_split_clause,[],[f560,f901]) ).
fof(f901,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f560,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(f899,plain,
spl0_63,
inference(avatar_split_clause,[],[f559,f896]) ).
fof(f896,plain,
( spl0_63
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f559,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(f894,plain,
spl0_62,
inference(avatar_split_clause,[],[f558,f891]) ).
fof(f891,plain,
( spl0_62
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f558,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(f889,plain,
spl0_61,
inference(avatar_split_clause,[],[f557,f886]) ).
fof(f886,plain,
( spl0_61
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f557,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f884,plain,
spl0_60,
inference(avatar_split_clause,[],[f556,f881]) ).
fof(f881,plain,
( spl0_60
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f556,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f879,plain,
spl0_59,
inference(avatar_split_clause,[],[f555,f876]) ).
fof(f876,plain,
( spl0_59
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f555,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(f874,plain,
spl0_58,
inference(avatar_split_clause,[],[f554,f871]) ).
fof(f871,plain,
( spl0_58
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f554,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f869,plain,
spl0_57,
inference(avatar_split_clause,[],[f553,f866]) ).
fof(f866,plain,
( spl0_57
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f553,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f864,plain,
spl0_56,
inference(avatar_split_clause,[],[f552,f861]) ).
fof(f861,plain,
( spl0_56
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f552,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f859,plain,
spl0_55,
inference(avatar_split_clause,[],[f551,f856]) ).
fof(f551,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f854,plain,
spl0_54,
inference(avatar_split_clause,[],[f550,f851]) ).
fof(f550,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f849,plain,
spl0_53,
inference(avatar_split_clause,[],[f549,f846]) ).
fof(f846,plain,
( spl0_53
<=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f549,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Nat_Osemiring__char__0) ).
fof(f844,plain,
spl0_52,
inference(avatar_split_clause,[],[f548,f841]) ).
fof(f841,plain,
( spl0_52
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f548,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f839,plain,
spl0_51,
inference(avatar_split_clause,[],[f547,f836]) ).
fof(f836,plain,
( spl0_51
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f547,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(f834,plain,
spl0_50,
inference(avatar_split_clause,[],[f546,f831]) ).
fof(f831,plain,
( spl0_50
<=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f546,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
fof(f829,plain,
spl0_49,
inference(avatar_split_clause,[],[f545,f826]) ).
fof(f826,plain,
( spl0_49
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f545,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f824,plain,
spl0_48,
inference(avatar_split_clause,[],[f544,f821]) ).
fof(f821,plain,
( spl0_48
<=> class_RealVector_Ometric__space(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f544,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
fof(f819,plain,
spl0_47,
inference(avatar_split_clause,[],[f543,f816]) ).
fof(f816,plain,
( spl0_47
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f543,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f814,plain,
spl0_46,
inference(avatar_split_clause,[],[f542,f811]) ).
fof(f811,plain,
( spl0_46
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f542,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(f809,plain,
spl0_45,
inference(avatar_split_clause,[],[f541,f806]) ).
fof(f806,plain,
( spl0_45
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f541,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(f804,plain,
spl0_44,
inference(avatar_split_clause,[],[f540,f801]) ).
fof(f801,plain,
( spl0_44
<=> class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f540,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(f799,plain,
spl0_43,
inference(avatar_split_clause,[],[f539,f796]) ).
fof(f796,plain,
( spl0_43
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f539,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(f794,plain,
spl0_42,
inference(avatar_split_clause,[],[f538,f791]) ).
fof(f538,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(f789,plain,
spl0_41,
inference(avatar_split_clause,[],[f537,f786]) ).
fof(f786,plain,
( spl0_41
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f537,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f784,plain,
spl0_40,
inference(avatar_split_clause,[],[f536,f781]) ).
fof(f781,plain,
( spl0_40
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f536,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f779,plain,
spl0_39,
inference(avatar_split_clause,[],[f535,f776]) ).
fof(f776,plain,
( spl0_39
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f535,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(f774,plain,
spl0_38,
inference(avatar_split_clause,[],[f534,f771]) ).
fof(f771,plain,
( spl0_38
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f534,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(f769,plain,
spl0_37,
inference(avatar_split_clause,[],[f533,f766]) ).
fof(f766,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f533,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(f764,plain,
spl0_36,
inference(avatar_split_clause,[],[f532,f761]) ).
fof(f761,plain,
( spl0_36
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f532,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f759,plain,
spl0_35,
inference(avatar_split_clause,[],[f531,f756]) ).
fof(f756,plain,
( spl0_35
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f531,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f754,plain,
spl0_34,
inference(avatar_split_clause,[],[f530,f751]) ).
fof(f751,plain,
( spl0_34
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f530,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f749,plain,
spl0_33,
inference(avatar_split_clause,[],[f529,f746]) ).
fof(f746,plain,
( spl0_33
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f529,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(f744,plain,
spl0_32,
inference(avatar_split_clause,[],[f528,f741]) ).
fof(f741,plain,
( spl0_32
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f528,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(f739,plain,
spl0_31,
inference(avatar_split_clause,[],[f527,f736]) ).
fof(f527,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(f734,plain,
spl0_30,
inference(avatar_split_clause,[],[f526,f731]) ).
fof(f731,plain,
( spl0_30
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f526,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(f729,plain,
spl0_29,
inference(avatar_split_clause,[],[f525,f726]) ).
fof(f726,plain,
( spl0_29
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f525,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(f724,plain,
spl0_28,
inference(avatar_split_clause,[],[f524,f721]) ).
fof(f721,plain,
( spl0_28
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f524,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f719,plain,
spl0_27,
inference(avatar_split_clause,[],[f523,f716]) ).
fof(f716,plain,
( spl0_27
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f523,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(f714,plain,
spl0_26,
inference(avatar_split_clause,[],[f522,f711]) ).
fof(f711,plain,
( spl0_26
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f522,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(f709,plain,
spl0_25,
inference(avatar_split_clause,[],[f521,f706]) ).
fof(f706,plain,
( spl0_25
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f521,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f704,plain,
spl0_24,
inference(avatar_split_clause,[],[f520,f701]) ).
fof(f701,plain,
( spl0_24
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f520,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(f699,plain,
spl0_23,
inference(avatar_split_clause,[],[f519,f696]) ).
fof(f696,plain,
( spl0_23
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f519,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(f694,plain,
spl0_22,
inference(avatar_split_clause,[],[f518,f691]) ).
fof(f691,plain,
( spl0_22
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f518,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(f689,plain,
spl0_21,
inference(avatar_split_clause,[],[f517,f686]) ).
fof(f686,plain,
( spl0_21
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f517,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(f684,plain,
spl0_20,
inference(avatar_split_clause,[],[f516,f681]) ).
fof(f681,plain,
( spl0_20
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f516,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(f679,plain,
spl0_19,
inference(avatar_split_clause,[],[f515,f676]) ).
fof(f676,plain,
( spl0_19
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f515,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(f674,plain,
spl0_18,
inference(avatar_split_clause,[],[f514,f671]) ).
fof(f671,plain,
( spl0_18
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f514,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(f669,plain,
spl0_17,
inference(avatar_split_clause,[],[f513,f666]) ).
fof(f666,plain,
( spl0_17
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f513,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f664,plain,
spl0_16,
inference(avatar_split_clause,[],[f512,f661]) ).
fof(f661,plain,
( spl0_16
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f512,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f659,plain,
spl0_15,
inference(avatar_split_clause,[],[f511,f656]) ).
fof(f656,plain,
( spl0_15
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f511,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f654,plain,
spl0_14,
inference(avatar_split_clause,[],[f510,f651]) ).
fof(f651,plain,
( spl0_14
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f510,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f649,plain,
spl0_13,
inference(avatar_split_clause,[],[f509,f646]) ).
fof(f646,plain,
( spl0_13
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f509,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f644,plain,
spl0_12,
inference(avatar_split_clause,[],[f508,f641]) ).
fof(f641,plain,
( spl0_12
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f508,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f639,plain,
spl0_11,
inference(avatar_split_clause,[],[f507,f636]) ).
fof(f636,plain,
( spl0_11
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f507,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f634,plain,
spl0_10,
inference(avatar_split_clause,[],[f506,f631]) ).
fof(f631,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f506,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f629,plain,
spl0_9,
inference(avatar_split_clause,[],[f505,f626]) ).
fof(f626,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f505,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(f624,plain,
spl0_8,
inference(avatar_split_clause,[],[f504,f621]) ).
fof(f621,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f504,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f619,plain,
spl0_7,
inference(avatar_split_clause,[],[f503,f616]) ).
fof(f616,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f503,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(f614,plain,
spl0_6,
inference(avatar_split_clause,[],[f502,f611]) ).
fof(f611,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f502,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f609,plain,
spl0_5,
inference(avatar_split_clause,[],[f501,f606]) ).
fof(f606,plain,
( spl0_5
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f501,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f604,plain,
spl0_4,
inference(avatar_split_clause,[],[f500,f601]) ).
fof(f601,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f500,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(f599,plain,
spl0_3,
inference(avatar_split_clause,[],[f499,f596]) ).
fof(f596,plain,
( spl0_3
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f499,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(f594,plain,
spl0_2,
inference(avatar_split_clause,[],[f498,f591]) ).
fof(f591,plain,
( spl0_2
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f498,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(f589,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f497,f586]) ).
fof(f497,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(v_c____,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG384-1 : TPTP v8.1.2. Released v4.1.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 19:57:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (13540)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (13543)WARNING: value z3 for option sas not known
% 0.15/0.40 % (13543)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 % (13542)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 % (13546)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.40 % (13545)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 % (13547)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 % (13544)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40 % (13541)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.45 % (13545)First to succeed.
% 0.21/0.45 TRYING [1]
% 0.21/0.45 % (13545)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13540"
% 0.21/0.46 % (13545)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (13545)------------------------------
% 0.21/0.46 % (13545)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46 % (13545)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (13545)Memory used [KB]: 2101
% 0.21/0.46 % (13545)Time elapsed: 0.054 s
% 0.21/0.46 % (13545)Instructions burned: 103 (million)
% 0.21/0.46 % (13540)Success in time 0.097 s
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