TSTP Solution File: ALG361-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG361-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:37:14 EDT 2024
% Result : Unsatisfiable 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 602
% Syntax : Number of formulae : 957 ( 408 unt; 0 def)
% Number of atoms : 1962 ( 220 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1694 ( 689 ~; 695 |; 0 &)
% ( 310 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 371 ( 369 usr; 312 prp; 0-5 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-5 aty)
% Number of variables : 945 ( 945 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3382,plain,
$false,
inference(avatar_sat_refutation,[],[f606,f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f751,f756,f761,f766,f771,f776,f781,f786,f791,f796,f801,f806,f811,f816,f821,f826,f831,f836,f841,f846,f851,f856,f861,f866,f871,f876,f881,f886,f891,f896,f901,f906,f911,f916,f921,f926,f931,f936,f941,f946,f951,f956,f961,f966,f971,f976,f981,f986,f991,f995,f1000,f1004,f1008,f1012,f1017,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1074,f1079,f1084,f1089,f1093,f1097,f1101,f1105,f1111,f1116,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1161,f1179,f1183,f1187,f1191,f1196,f1200,f1204,f1208,f1213,f1217,f1232,f1236,f1240,f1244,f1248,f1252,f1256,f1260,f1264,f1268,f1272,f1276,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1341,f1345,f1349,f1372,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1505,f1509,f1513,f1517,f1521,f1525,f1529,f1533,f1537,f1541,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1625,f1643,f1719,f1723,f1727,f1731,f1735,f1741,f1745,f1749,f1753,f1757,f1761,f1792,f1869,f1873,f1877,f1882,f1886,f1890,f1894,f1898,f1902,f1906,f1910,f1914,f1918,f1922,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1964,f1968,f1973,f2045,f2195,f2247,f2251,f2255,f2259,f2263,f2267,f2271,f2276,f2280,f2284,f2288,f2292,f2296,f2300,f2304,f2308,f2312,f2316,f2320,f2324,f2328,f2332,f2336,f2340,f2344,f2348,f2352,f2356,f2364,f2368,f2372,f2376,f2380,f2384,f2388,f2392,f2396,f2400,f2410,f2414,f2418,f2953,f3058,f3062,f3066,f3070,f3074,f3078,f3082,f3109,f3113,f3117,f3121,f3125,f3129,f3133,f3137,f3141,f3145,f3176,f3180,f3184,f3188,f3192,f3196,f3200,f3204,f3208,f3212,f3243,f3381]) ).
fof(f3381,plain,
( ~ spl0_80
| ~ spl0_236
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f3244,f3241,f1961,f997]) ).
fof(f997,plain,
( spl0_80
<=> c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1961,plain,
( spl0_236
<=> c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f3241,plain,
( spl0_310
<=> ! [X6] :
( ~ c_SEQ_Osubseq(X6)
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,X6,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3244,plain,
( ~ c_SEQ_Osubseq(v_sko__CHAINED__1(v_s))
| ~ spl0_236
| ~ spl0_310 ),
inference(resolution,[],[f3242,f1963]) ).
fof(f1963,plain,
( c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ spl0_236 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f3242,plain,
( ! [X6] :
( ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,X6,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(X6) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f3241]) ).
fof(f3243,plain,
( spl0_310
| spl0_1 ),
inference(avatar_split_clause,[],[f509,f603,f3241]) ).
fof(f603,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f509,axiom,
! [X6] :
( v_thesis____
| ~ c_SEQ_Osubseq(X6)
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,X6,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
fof(f3212,plain,
spl0_309,
inference(avatar_split_clause,[],[f501,f3210]) ).
fof(f3210,plain,
( spl0_309
<=> ! [X5,X0,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_ORe,X5,tc_Complex_Ocomplex,tc_RealDef_Oreal,X0),X33,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f501,axiom,
! [X0,X5,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_ORe,X5,tc_Complex_Ocomplex,tc_RealDef_Oreal,X0),X33,X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZfun_0) ).
fof(f3208,plain,
spl0_308,
inference(avatar_split_clause,[],[f499,f3206]) ).
fof(f3206,plain,
( spl0_308
<=> ! [X25,X1] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f499,axiom,
! [X1,X25] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OLIMSEQ_0) ).
fof(f3204,plain,
spl0_307,
inference(avatar_split_clause,[],[f486,f3202]) ).
fof(f3202,plain,
( spl0_307
<=> ! [X25,X1] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f486,axiom,
! [X1,X25] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osums_0) ).
fof(f3200,plain,
spl0_306,
inference(avatar_split_clause,[],[f474,f3198]) ).
fof(f3198,plain,
( spl0_306
<=> ! [X25,X1] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f474,axiom,
! [X1,X25] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OLIMSEQ_0) ).
fof(f3196,plain,
spl0_305,
inference(avatar_split_clause,[],[f421,f3194]) ).
fof(f3194,plain,
( spl0_305
<=> ! [X25,X1] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X1),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f421,axiom,
! [X1,X25] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osums_0) ).
fof(f3192,plain,
spl0_304,
inference(avatar_split_clause,[],[f419,f3190]) ).
fof(f3190,plain,
( spl0_304
<=> ! [X5,X0,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_OIm,X5,tc_Complex_Ocomplex,tc_RealDef_Oreal,X0),X33,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f419,axiom,
! [X0,X5,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_OIm,X5,tc_Complex_Ocomplex,tc_RealDef_Oreal,X0),X33,X0,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZfun_0) ).
fof(f3188,plain,
spl0_303,
inference(avatar_split_clause,[],[f340,f3186]) ).
fof(f3186,plain,
( spl0_303
<=> ! [X6,X25,X0] :
( ~ c_SEQ_Osubseq(X6)
| ~ class_RealVector_Ometric__space(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_Fun_Ocomp(X25,X6,tc_nat,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f340,axiom,
! [X0,X6,X25] :
( ~ c_SEQ_Osubseq(X6)
| ~ class_RealVector_Ometric__space(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_Fun_Ocomp(X25,X6,tc_nat,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cauchy__subseq__Cauchy_0) ).
fof(f3184,plain,
spl0_302,
inference(avatar_split_clause,[],[f335,f3182]) ).
fof(f3182,plain,
( spl0_302
<=> ! [X25,X1] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X1),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f335,axiom,
! [X1,X25] :
( ~ c_SEQ_OLIMSEQ(X25,X1,tc_Complex_Ocomplex)
| c_SEQ_OLIMSEQ(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X1),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OLIMSEQ_0) ).
fof(f3180,plain,
spl0_301,
inference(avatar_split_clause,[],[f334,f3178]) ).
fof(f3178,plain,
( spl0_301
<=> ! [X25,X1] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X1),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f334,axiom,
! [X1,X25] :
( ~ c_Series_Osums(X25,X1,tc_Complex_Ocomplex)
| c_Series_Osums(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X1),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osums_0) ).
fof(f3176,plain,
spl0_300,
inference(avatar_split_clause,[],[f329,f3174]) ).
fof(f3174,plain,
( spl0_300
<=> ! [X5,X0,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_Ocnj,X5,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X0),X33,X0,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f329,axiom,
! [X0,X5,X33] :
( ~ c_Limits_OZfun(X5,X33,X0,tc_Complex_Ocomplex)
| c_Limits_OZfun(c_COMBB(c_Complex_Ocnj,X5,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X0),X33,X0,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZfun_0) ).
fof(f3145,plain,
spl0_299,
inference(avatar_split_clause,[],[f288,f3143]) ).
fof(f3143,plain,
( spl0_299
<=> ! [X25,X0,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f288,axiom,
! [X0,X8,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OCauchy_0) ).
fof(f3141,plain,
spl0_298,
inference(avatar_split_clause,[],[f286,f3139]) ).
fof(f3139,plain,
( spl0_298
<=> ! [X25,X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f286,axiom,
! [X0,X9,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_SEQ_OCauchy(X25,X0)
| c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OCauchy_0) ).
fof(f3137,plain,
spl0_297,
inference(avatar_split_clause,[],[f279,f3135]) ).
fof(f3135,plain,
( spl0_297
<=> ! [X25,X0,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f279,axiom,
! [X0,X8,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OZseq_0) ).
fof(f3133,plain,
spl0_296,
inference(avatar_split_clause,[],[f277,f3131]) ).
fof(f3131,plain,
( spl0_296
<=> ! [X25,X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f277,axiom,
! [X0,X9,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OZseq_0) ).
fof(f3129,plain,
spl0_295,
inference(avatar_split_clause,[],[f267,f3127]) ).
fof(f3127,plain,
( spl0_295
<=> ! [X25,X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f267,axiom,
! [X0,X9,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X9,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Osummable_0) ).
fof(f3125,plain,
spl0_294,
inference(avatar_split_clause,[],[f265,f3123]) ).
fof(f3123,plain,
( spl0_294
<=> ! [X25,X0,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f265,axiom,
! [X0,X8,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X8,X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Osummable_0) ).
fof(f3121,plain,
spl0_293,
inference(avatar_split_clause,[],[f247,f3119]) ).
fof(f3119,plain,
( spl0_293
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f247,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3117,plain,
spl0_292,
inference(avatar_split_clause,[],[f246,f3115]) ).
fof(f3115,plain,
( spl0_292
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f246,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3113,plain,
spl0_291,
inference(avatar_split_clause,[],[f239,f3111]) ).
fof(f3111,plain,
( spl0_291
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f239,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
fof(f3109,plain,
spl0_290,
inference(avatar_split_clause,[],[f238,f3107]) ).
fof(f3107,plain,
( spl0_290
<=> ! [X9,X0,X21] :
( ~ class_RealVector_Oreal__vector(X0)
| hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X9) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f238,axiom,
! [X21,X0,X9] :
( ~ class_RealVector_Oreal__vector(X0)
| hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X9) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
fof(f3082,plain,
spl0_289,
inference(avatar_split_clause,[],[f230,f3080]) ).
fof(f3080,plain,
( spl0_289
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f230,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f3078,plain,
spl0_288,
inference(avatar_split_clause,[],[f158,f3076]) ).
fof(f3076,plain,
( spl0_288
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f158,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3074,plain,
spl0_287,
inference(avatar_split_clause,[],[f157,f3072]) ).
fof(f3072,plain,
( spl0_287
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f157,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3070,plain,
spl0_286,
inference(avatar_split_clause,[],[f105,f3068]) ).
fof(f3068,plain,
( spl0_286
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f3066,plain,
spl0_285,
inference(avatar_split_clause,[],[f104,f3064]) ).
fof(f3064,plain,
( spl0_285
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f104,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f3062,plain,
spl0_284,
inference(avatar_split_clause,[],[f68,f3060]) ).
fof(f3060,plain,
( spl0_284
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f3058,plain,
spl0_283,
inference(avatar_split_clause,[],[f67,f3056]) ).
fof(f3056,plain,
( spl0_283
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f67,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f2953,plain,
( spl0_282
| ~ spl0_162
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2020,f1888,f1436,f2951]) ).
fof(f2951,plain,
( spl0_282
<=> ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f1436,plain,
( spl0_162
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1888,plain,
( spl0_218
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2020,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_162
| ~ spl0_218 ),
inference(duplicate_literal_removal,[],[f2002]) ).
fof(f2002,plain,
( ! [X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_162
| ~ spl0_218 ),
inference(resolution,[],[f1889,f1437]) ).
fof(f1437,plain,
( ! [X0] :
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1436]) ).
fof(f1889,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X2,X0)
| c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1888]) ).
fof(f2418,plain,
spl0_281,
inference(avatar_split_clause,[],[f508,f2416]) ).
fof(f2416,plain,
( spl0_281
<=> ! [X4,X53,X7,X0,X52,X46] : hAPP(c_COMBB(X46,X52,X4,X0,X7),X53) = hAPP(X46,hAPP(X52,X53)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f508,axiom,
! [X46,X0,X7,X52,X4,X53] : hAPP(c_COMBB(X46,X52,X4,X0,X7),X53) = hAPP(X46,hAPP(X52,X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
fof(f2414,plain,
spl0_280,
inference(avatar_split_clause,[],[f505,f2412]) ).
fof(f2412,plain,
( spl0_280
<=> ! [X6,X36,X37] :
( ~ c_SEQ_Osubseq(X6)
| ~ c_HOL_Oord__class_Oless(X36,X37,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(X6,X36),hAPP(X6,X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f505,axiom,
! [X36,X37,X6] :
( ~ c_SEQ_Osubseq(X6)
| ~ c_HOL_Oord__class_Oless(X36,X37,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(X6,X36),hAPP(X6,X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subseq__def_0) ).
fof(f2410,plain,
spl0_279,
inference(avatar_split_clause,[],[f471,f2408]) ).
fof(f2408,plain,
( spl0_279
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X21,X9,X0)
| ~ c_lessequals(X22,X21,X0)
| c_lessequals(X22,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f471,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X21,X9,X0)
| ~ c_lessequals(X22,X21,X0)
| c_lessequals(X22,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f2400,plain,
spl0_278,
inference(avatar_split_clause,[],[f470,f2398]) ).
fof(f2398,plain,
( spl0_278
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_lessequals(X22,X21,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f470,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_lessequals(X22,X21,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f2396,plain,
spl0_277,
inference(avatar_split_clause,[],[f469,f2394]) ).
fof(f2394,plain,
( spl0_277
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X22,X21,X0)
| ~ c_lessequals(X21,X9,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f469,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X22,X21,X0)
| ~ c_lessequals(X21,X9,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f2392,plain,
spl0_276,
inference(avatar_split_clause,[],[f468,f2390]) ).
fof(f2390,plain,
( spl0_276
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X21,X0)
| ~ c_lessequals(X21,X22,X0)
| c_lessequals(X9,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f468,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X21,X0)
| ~ c_lessequals(X21,X22,X0)
| c_lessequals(X9,X22,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f2388,plain,
spl0_275,
inference(avatar_split_clause,[],[f467,f2386]) ).
fof(f2386,plain,
( spl0_275
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_lessequals(X21,X22,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f467,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_lessequals(X21,X22,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f2384,plain,
spl0_274,
inference(avatar_split_clause,[],[f466,f2382]) ).
fof(f2382,plain,
( spl0_274
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X22,X0)
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f466,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X22,X0)
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f2380,plain,
spl0_273,
inference(avatar_split_clause,[],[f449,f2378]) ).
fof(f2378,plain,
( spl0_273
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f449,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f2376,plain,
spl0_272,
inference(avatar_split_clause,[],[f402,f2374]) ).
fof(f2374,plain,
( spl0_272
<=> ! [X9,X0,X21] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X9 = X21
| hAPP(c_RealVector_Oof__real(X0),X9) != hAPP(c_RealVector_Oof__real(X0),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f402,axiom,
! [X21,X0,X9] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| X9 = X21
| hAPP(c_RealVector_Oof__real(X0),X9) != hAPP(c_RealVector_Oof__real(X0),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
fof(f2372,plain,
spl0_271,
inference(avatar_split_clause,[],[f399,f2370]) ).
fof(f2370,plain,
( spl0_271
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_HOL_Oord__class_Oless(X22,X21,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f399,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_HOL_Oord__class_Oless(X22,X21,X0)
| c_HOL_Oord__class_Oless(X22,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f2368,plain,
spl0_270,
inference(avatar_split_clause,[],[f398,f2366]) ).
fof(f2366,plain,
( spl0_270
<=> ! [X0,X21,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_HOL_Oord__class_Oless(X21,X22,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f398,axiom,
! [X21,X0,X9,X22] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_HOL_Oord__class_Oless(X21,X22,X0)
| c_HOL_Oord__class_Oless(X9,X22,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f2364,plain,
spl0_269,
inference(avatar_split_clause,[],[f364,f2362]) ).
fof(f2362,plain,
( spl0_269
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f364,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2356,plain,
spl0_268,
inference(avatar_split_clause,[],[f363,f2354]) ).
fof(f2354,plain,
( spl0_268
<=> ! [X9,X0,X21] :
( ~ class_Lattices_Oboolean__algebra(X0)
| X9 = X21
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f363,axiom,
! [X21,X0,X9] :
( ~ class_Lattices_Oboolean__algebra(X0)
| X9 = X21
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
fof(f2352,plain,
spl0_267,
inference(avatar_split_clause,[],[f352,f2350]) ).
fof(f2350,plain,
( spl0_267
<=> ! [X25,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f352,axiom,
! [X0,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X25,X0)
| c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__minus_0) ).
fof(f2348,plain,
spl0_266,
inference(avatar_split_clause,[],[f348,f2346]) ).
fof(f2346,plain,
( spl0_266
<=> ! [X25,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X25,X0,X0,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f348,axiom,
! [X0,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(X0),X25,X0,X0,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__minus_0) ).
fof(f2344,plain,
spl0_265,
inference(avatar_split_clause,[],[f314,f2342]) ).
fof(f2342,plain,
( spl0_265
<=> ! [X6,X0] :
( ~ class_SEQ_Obanach(X0)
| c_Series_Osummable(X6,X0)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X6,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f314,axiom,
! [X0,X6] :
( ~ class_SEQ_Obanach(X0)
| c_Series_Osummable(X6,X0)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X6,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__norm__cancel_0) ).
fof(f2340,plain,
spl0_264,
inference(avatar_split_clause,[],[f304,f2338]) ).
fof(f2338,plain,
( spl0_264
<=> ! [X25,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X25,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f304,axiom,
! [X0,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_SEQ_OZseq(X25,X0)
| c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X25,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__norm__iff_1) ).
fof(f2336,plain,
spl0_263,
inference(avatar_split_clause,[],[f303,f2334]) ).
fof(f2334,plain,
( spl0_263
<=> ! [X25,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_SEQ_OZseq(X25,X0)
| ~ c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X25,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f303,axiom,
! [X0,X25] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_SEQ_OZseq(X25,X0)
| ~ c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X0),X25,X0,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zseq__norm__iff_0) ).
fof(f2332,plain,
spl0_262,
inference(avatar_split_clause,[],[f298,f2330]) ).
fof(f2330,plain,
( spl0_262
<=> ! [X25,X37,X36] :
( ~ c_SEQ_Odecseq(X25)
| ~ c_lessequals(X36,X37,tc_nat)
| c_lessequals(hAPP(X25,X37),hAPP(X25,X36),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f298,axiom,
! [X36,X37,X25] :
( ~ c_SEQ_Odecseq(X25)
| ~ c_lessequals(X36,X37,tc_nat)
| c_lessequals(hAPP(X25,X37),hAPP(X25,X36),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__def_0) ).
fof(f2328,plain,
spl0_261,
inference(avatar_split_clause,[],[f297,f2326]) ).
fof(f2326,plain,
( spl0_261
<=> ! [X25,X37,X36] :
( ~ c_SEQ_Oincseq(X25)
| ~ c_lessequals(X36,X37,tc_nat)
| c_lessequals(hAPP(X25,X36),hAPP(X25,X37),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f297,axiom,
! [X36,X37,X25] :
( ~ c_SEQ_Oincseq(X25)
| ~ c_lessequals(X36,X37,tc_nat)
| c_lessequals(hAPP(X25,X36),hAPP(X25,X37),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__def_0) ).
fof(f2324,plain,
spl0_260,
inference(avatar_split_clause,[],[f249,f2322]) ).
fof(f2322,plain,
( spl0_260
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f249,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f2320,plain,
spl0_259,
inference(avatar_split_clause,[],[f248,f2318]) ).
fof(f2318,plain,
( spl0_259
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f248,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f2316,plain,
spl0_258,
inference(avatar_split_clause,[],[f156,f2314]) ).
fof(f2314,plain,
( spl0_258
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X0),X9),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f156,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X0),X9),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
fof(f2312,plain,
spl0_257,
inference(avatar_split_clause,[],[f125,f2310]) ).
fof(f2310,plain,
( spl0_257
<=> ! [X9,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OLIM(c_HOL_Otimes__class_Otimes(X9,X0),X1,hAPP(c_HOL_Otimes__class_Otimes(X9,X0),X1),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f125,axiom,
! [X0,X1,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OLIM(c_HOL_Otimes__class_Otimes(X9,X0),X1,hAPP(c_HOL_Otimes__class_Otimes(X9,X0),X1),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ocont_0) ).
fof(f2308,plain,
spl0_256,
inference(avatar_split_clause,[],[f118,f2306]) ).
fof(f2306,plain,
( spl0_256
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
fof(f2304,plain,
spl0_255,
inference(avatar_split_clause,[],[f97,f2302]) ).
fof(f2302,plain,
( spl0_255
<=> ! [X1,X4,X0,X16,X2,X7] : hAPP(X1,hAPP(X2,X16)) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X0),X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f97,axiom,
! [X2,X0,X1,X16,X7,X4] : hAPP(X1,hAPP(X2,X16)) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X0),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f2300,plain,
spl0_254,
inference(avatar_split_clause,[],[f89,f2298]) ).
fof(f2298,plain,
( spl0_254
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| hAPP(c_RealVector_Onorm__class_Onorm(X0),X9) = hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f89,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| hAPP(c_RealVector_Onorm__class_Onorm(X0),X9) = hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
fof(f2296,plain,
spl0_253,
inference(avatar_split_clause,[],[f88,f2294]) ).
fof(f2294,plain,
( spl0_253
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f88,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f2292,plain,
spl0_252,
inference(avatar_split_clause,[],[f87,f2290]) ).
fof(f2290,plain,
( spl0_252
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = hAPP(c_HOL_Oabs__class_Oabs(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f87,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = hAPP(c_HOL_Oabs__class_Oabs(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2288,plain,
spl0_251,
inference(avatar_split_clause,[],[f85,f2286]) ).
fof(f2286,plain,
( spl0_251
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f85,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f2284,plain,
spl0_250,
inference(avatar_split_clause,[],[f84,f2282]) ).
fof(f2282,plain,
( spl0_250
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f84,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f2280,plain,
spl0_249,
inference(avatar_split_clause,[],[f83,f2278]) ).
fof(f2278,plain,
( spl0_249
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f83,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f2276,plain,
( spl0_248
| ~ spl0_75
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1360,f1262,f973,f2273]) ).
fof(f2273,plain,
( spl0_248
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f973,plain,
( spl0_75
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1262,plain,
( spl0_137
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1360,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_75
| ~ spl0_137 ),
inference(resolution,[],[f1263,f975]) ).
fof(f975,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f1263,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1262]) ).
fof(f2271,plain,
spl0_247,
inference(avatar_split_clause,[],[f82,f2269]) ).
fof(f2269,plain,
( spl0_247
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f82,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f2267,plain,
spl0_246,
inference(avatar_split_clause,[],[f81,f2265]) ).
fof(f2265,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f81,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
fof(f2263,plain,
spl0_245,
inference(avatar_split_clause,[],[f80,f2261]) ).
fof(f2261,plain,
( spl0_245
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f80,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
fof(f2259,plain,
spl0_244,
inference(avatar_split_clause,[],[f79,f2257]) ).
fof(f2257,plain,
( spl0_244
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f79,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
fof(f2255,plain,
spl0_243,
inference(avatar_split_clause,[],[f78,f2253]) ).
fof(f2253,plain,
( spl0_243
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f78,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X1,hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
fof(f2251,plain,
spl0_242,
inference(avatar_split_clause,[],[f57,f2249]) ).
fof(f2249,plain,
( spl0_242
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = hAPP(c_HOL_Oabs__class_Oabs(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f57,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = hAPP(c_HOL_Oabs__class_Oabs(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2247,plain,
spl0_241,
inference(avatar_split_clause,[],[f12,f2245]) ).
fof(f2245,plain,
( spl0_241
<=> ! [X0,X1,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1,hAPP(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f12,axiom,
! [X0,X1,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1,hAPP(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Ocont_0) ).
fof(f2195,plain,
( spl0_240
| ~ spl0_52
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1359,f1262,f858,f2192]) ).
fof(f2192,plain,
( spl0_240
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f858,plain,
( spl0_52
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1359,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_52
| ~ spl0_137 ),
inference(resolution,[],[f1263,f860]) ).
fof(f860,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f858]) ).
fof(f2045,plain,
( spl0_239
| ~ spl0_23
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1354,f1246,f713,f2042]) ).
fof(f2042,plain,
( spl0_239
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f713,plain,
( spl0_23
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1246,plain,
( spl0_133
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1354,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_HOL_Oabs__class_Oabs(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_23
| ~ spl0_133 ),
inference(resolution,[],[f1247,f715]) ).
fof(f715,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1247,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f1973,plain,
( spl0_238
| ~ spl0_69
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1353,f1242,f943,f1970]) ).
fof(f1970,plain,
( spl0_238
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f943,plain,
( spl0_69
<=> class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1242,plain,
( spl0_132
<=> ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_Oof__real(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1353,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_69
| ~ spl0_132 ),
inference(resolution,[],[f1243,f945]) ).
fof(f945,plain,
( class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f1243,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_Oof__real(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) )
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f1968,plain,
spl0_237,
inference(avatar_split_clause,[],[f599,f1966]) ).
fof(f1966,plain,
( spl0_237
<=> ! [X22] : hAPP(c_Complex_Ocnj,X22) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X22),hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X22))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f599,plain,
! [X22] : hAPP(c_Complex_Ocnj,X22) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X22),hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X22))),
inference(forward_demodulation,[],[f385,f344]) ).
fof(f344,axiom,
! [X9] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X9)) = hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Im__cnj_0) ).
fof(f385,axiom,
! [X22] : hAPP(c_Complex_Ocnj,X22) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X22),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X22))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj__def_0) ).
fof(f1964,plain,
spl0_236,
inference(avatar_split_clause,[],[f511,f1961]) ).
fof(f511,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f1959,plain,
spl0_235,
inference(avatar_split_clause,[],[f434,f1957]) ).
fof(f1957,plain,
( spl0_235
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f434,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
fof(f1955,plain,
spl0_234,
inference(avatar_split_clause,[],[f426,f1953]) ).
fof(f1953,plain,
( spl0_234
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Oorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f426,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| c_HOL_Oord__class_Oless(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
fof(f1951,plain,
spl0_233,
inference(avatar_split_clause,[],[f418,f1949]) ).
fof(f1949,plain,
( spl0_233
<=> ! [X9,X0,X21] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_HOL_Oord__class_Oless(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f418,axiom,
! [X21,X0,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_HOL_Oord__class_Oless(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f1947,plain,
spl0_232,
inference(avatar_split_clause,[],[f410,f1945]) ).
fof(f1945,plain,
( spl0_232
<=> ! [X0,X25,X2,X1] :
( ~ class_RealVector_Ometric__space(X0)
| X1 = X2
| ~ c_SEQ_OLIMSEQ(X25,X1,X0)
| ~ c_SEQ_OLIMSEQ(X25,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f410,axiom,
! [X2,X0,X1,X25] :
( ~ class_RealVector_Ometric__space(X0)
| X1 = X2
| ~ c_SEQ_OLIMSEQ(X25,X1,X0)
| ~ c_SEQ_OLIMSEQ(X25,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__unique_0) ).
fof(f1943,plain,
spl0_231,
inference(avatar_split_clause,[],[f407,f1941]) ).
fof(f1941,plain,
( spl0_231
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Oorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| ~ c_lessequals(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f407,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| X9 = X21
| ~ c_lessequals(X9,X21,X0)
| ~ c_lessequals(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f1939,plain,
spl0_230,
inference(avatar_split_clause,[],[f406,f1937]) ).
fof(f1937,plain,
( spl0_230
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_HOL_Oord__class_Oless(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f406,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_HOL_Oord__class_Oless(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
fof(f1935,plain,
spl0_229,
inference(avatar_split_clause,[],[f404,f1933]) ).
fof(f1933,plain,
( spl0_229
<=> ! [X4,X9,X0,X6] :
( ~ class_RealVector_Ometric__space(X4)
| ~ class_RealVector_Ometric__space(X0)
| ~ c_Lim_OisUCont(X6,X0,X4)
| c_Lim_OisCont(X6,X9,X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f404,axiom,
! [X0,X6,X9,X4] :
( ~ class_RealVector_Ometric__space(X4)
| ~ class_RealVector_Ometric__space(X0)
| ~ c_Lim_OisUCont(X6,X0,X4)
| c_Lim_OisCont(X6,X9,X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_isUCont__isCont_0) ).
fof(f1931,plain,
spl0_228,
inference(avatar_split_clause,[],[f234,f1929]) ).
fof(f1929,plain,
( spl0_228
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Oabs__class_Oabs(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f234,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Oabs__class_Oabs(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f1927,plain,
( spl0_227
| ~ spl0_45
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1352,f1242,f823,f1924]) ).
fof(f1924,plain,
( spl0_227
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f823,plain,
( spl0_45
<=> class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1352,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Oof__real(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_45
| ~ spl0_132 ),
inference(resolution,[],[f1243,f825]) ).
fof(f825,plain,
( class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f823]) ).
fof(f1922,plain,
spl0_226,
inference(avatar_split_clause,[],[f231,f1920]) ).
fof(f1920,plain,
( spl0_226
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f231,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f1918,plain,
spl0_225,
inference(avatar_split_clause,[],[f201,f1916]) ).
fof(f1916,plain,
( spl0_225
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f201,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f1914,plain,
spl0_224,
inference(avatar_split_clause,[],[f198,f1912]) ).
fof(f1912,plain,
( spl0_224
<=> ! [X9] : hAPP(c_Complex_Ocnj,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_Complex_Ocnj,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f198,axiom,
! [X9] : hAPP(c_Complex_Ocnj,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_Complex_Ocnj,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ominus_0) ).
fof(f1910,plain,
spl0_223,
inference(avatar_split_clause,[],[f182,f1908]) ).
fof(f1908,plain,
( spl0_223
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f182,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f1906,plain,
spl0_222,
inference(avatar_split_clause,[],[f180,f1904]) ).
fof(f1904,plain,
( spl0_222
<=> ! [X4,X0,X6,X1] :
( ~ class_RealVector_Oreal__normed__vector(X4)
| ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_RealVector_Obounded__linear(X6,X0,X4)
| c_Lim_OisCont(X6,X1,X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f180,axiom,
! [X0,X1,X6,X4] :
( ~ class_RealVector_Oreal__normed__vector(X4)
| ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_RealVector_Obounded__linear(X6,X0,X4)
| c_Lim_OisCont(X6,X1,X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OisCont_0) ).
fof(f1902,plain,
spl0_221,
inference(avatar_split_clause,[],[f169,f1900]) ).
fof(f1900,plain,
( spl0_221
<=> ! [X9] : hAPP(c_Complex_ORe,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f169,axiom,
! [X9] : hAPP(c_Complex_ORe,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ominus_0) ).
fof(f1898,plain,
spl0_220,
inference(avatar_split_clause,[],[f167,f1896]) ).
fof(f1896,plain,
( spl0_220
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f167,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f1894,plain,
spl0_219,
inference(avatar_split_clause,[],[f162,f1892]) ).
fof(f1892,plain,
( spl0_219
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X2) = hAPP(c_HOL_Otimes__class_Otimes(X2,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f162,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X2) = hAPP(c_HOL_Otimes__class_Otimes(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f1890,plain,
spl0_218,
inference(avatar_split_clause,[],[f154,f1888]) ).
fof(f154,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,X2,X0)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
fof(f1886,plain,
spl0_217,
inference(avatar_split_clause,[],[f151,f1884]) ).
fof(f1884,plain,
( spl0_217
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1)),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f151,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1)),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
fof(f1882,plain,
( spl0_216
| ~ spl0_66
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1351,f1238,f928,f1879]) ).
fof(f1879,plain,
( spl0_216
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f928,plain,
( spl0_66
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1238,plain,
( spl0_131
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1351,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_66
| ~ spl0_131 ),
inference(resolution,[],[f1239,f930]) ).
fof(f930,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f1239,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(X0),c_HOL_Ozero__class_Ozero(X0)) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f1877,plain,
spl0_215,
inference(avatar_split_clause,[],[f150,f1875]) ).
fof(f1875,plain,
( spl0_215
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealVector_Onorm__class_Onorm(X0),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f150,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealVector_Onorm__class_Onorm(X0),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
fof(f1873,plain,
spl0_214,
inference(avatar_split_clause,[],[f115,f1871]) ).
fof(f1871,plain,
( spl0_214
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f115,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| hAPP(c_HOL_Oabs__class_Oabs(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
fof(f1869,plain,
spl0_213,
inference(avatar_split_clause,[],[f20,f1867]) ).
fof(f1867,plain,
( spl0_213
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X9
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_RealVector_Oof__real(X0),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f20,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X9
| c_HOL_Ozero__class_Ozero(X0) != hAPP(c_RealVector_Oof__real(X0),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
fof(f1792,plain,
( spl0_212
| ~ spl0_38
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1350,f1238,f788,f1789]) ).
fof(f1789,plain,
( spl0_212
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f788,plain,
( spl0_38
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1350,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl0_38
| ~ spl0_131 ),
inference(resolution,[],[f1239,f790]) ).
fof(f790,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f1761,plain,
spl0_211,
inference(avatar_split_clause,[],[f597,f1759]) ).
fof(f1759,plain,
( spl0_211
<=> ! [X9] : hAPP(c_Complex_OIm,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f597,plain,
! [X9] : hAPP(c_Complex_OIm,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X9)),
inference(forward_demodulation,[],[f49,f344]) ).
fof(f49,axiom,
! [X9] : hAPP(c_Complex_OIm,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X9)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ominus_0) ).
fof(f1757,plain,
spl0_210,
inference(avatar_split_clause,[],[f464,f1755]) ).
fof(f1755,plain,
( spl0_210
<=> ! [X32,X30,X31] :
( ~ c_lessequals(X30,X32,tc_nat)
| ~ c_lessequals(X32,X31,tc_nat)
| c_lessequals(X30,X31,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f464,axiom,
! [X31,X32,X30] :
( ~ c_lessequals(X30,X32,tc_nat)
| ~ c_lessequals(X32,X31,tc_nat)
| c_lessequals(X30,X31,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f1753,plain,
spl0_209,
inference(avatar_split_clause,[],[f344,f1751]) ).
fof(f1751,plain,
( spl0_209
<=> ! [X9] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X9)) = hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1749,plain,
spl0_208,
inference(avatar_split_clause,[],[f343,f1747]) ).
fof(f1747,plain,
( spl0_208
<=> ! [X2,X1] : hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f343,axiom,
! [X2,X1] : hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj_0) ).
fof(f1745,plain,
spl0_207,
inference(avatar_split_clause,[],[f338,f1743]) ).
fof(f1743,plain,
( spl0_207
<=> ! [X25,X37,X39] :
( ~ c_SEQ_Oincseq(X25)
| ~ c_SEQ_OLIMSEQ(X25,X39,tc_RealDef_Oreal)
| c_lessequals(hAPP(X25,X37),X39,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f338,axiom,
! [X39,X37,X25] :
( ~ c_SEQ_Oincseq(X25)
| ~ c_SEQ_OLIMSEQ(X25,X39,tc_RealDef_Oreal)
| c_lessequals(hAPP(X25,X37),X39,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__le_0) ).
fof(f1741,plain,
spl0_206,
inference(avatar_split_clause,[],[f337,f1739]) ).
fof(f1739,plain,
( spl0_206
<=> ! [X25,X37,X39] :
( ~ c_SEQ_Odecseq(X25)
| ~ c_SEQ_OLIMSEQ(X25,X39,tc_RealDef_Oreal)
| c_lessequals(X39,hAPP(X25,X37),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f337,axiom,
! [X39,X37,X25] :
( ~ c_SEQ_Odecseq(X25)
| ~ c_SEQ_OLIMSEQ(X25,X39,tc_RealDef_Oreal)
| c_lessequals(X39,hAPP(X25,X37),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__le_0) ).
fof(f1735,plain,
spl0_205,
inference(avatar_split_clause,[],[f293,f1733]) ).
fof(f1733,plain,
( spl0_205
<=> ! [X9,X21,X23] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X21
| c_Complex_Ocomplex_OComplex(X9,X21) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f293,axiom,
! [X21,X9,X23] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X21
| c_Complex_Ocomplex_OComplex(X9,X21) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_1) ).
fof(f1731,plain,
spl0_204,
inference(avatar_split_clause,[],[f236,f1729]) ).
fof(f1729,plain,
( spl0_204
<=> ! [X32,X30,X31] :
( ~ c_lessequals(X30,X32,tc_RealDef_Oreal)
| ~ c_lessequals(X32,X31,tc_RealDef_Oreal)
| c_lessequals(X30,X31,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f236,axiom,
! [X31,X32,X30] :
( ~ c_lessequals(X30,X32,tc_RealDef_Oreal)
| ~ c_lessequals(X32,X31,tc_RealDef_Oreal)
| c_lessequals(X30,X31,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f1727,plain,
spl0_203,
inference(avatar_split_clause,[],[f199,f1725]) ).
fof(f1725,plain,
( spl0_203
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f199,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
fof(f1723,plain,
spl0_202,
inference(avatar_split_clause,[],[f107,f1721]) ).
fof(f1721,plain,
( spl0_202
<=> ! [X6,X4,X0] :
( ~ class_RealVector_Oreal__normed__vector(X4)
| ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_RealVector_Obounded__linear(X6,X0,X4)
| c_Lim_OisUCont(X6,X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f107,axiom,
! [X0,X6,X4] :
( ~ class_RealVector_Oreal__normed__vector(X4)
| ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_RealVector_Obounded__linear(X6,X0,X4)
| c_Lim_OisUCont(X6,X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bounded__linear_OisUCont_0) ).
fof(f1719,plain,
spl0_201,
inference(avatar_split_clause,[],[f39,f1717]) ).
fof(f1717,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f39,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),X1) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f1643,plain,
( spl0_200
| ~ spl0_104
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1175,f1159,f1099,f1641]) ).
fof(f1641,plain,
( spl0_200
<=> ! [X0,X1] : c_Lim_OLIM(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X0,X1),X0,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1099,plain,
( spl0_104
<=> ! [X9,X21] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X9,X21)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1159,plain,
( spl0_118
<=> ! [X1] : c_Lim_OLIM(c_Complex_ORe,X1,hAPP(c_Complex_ORe,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1175,plain,
( ! [X0,X1] : c_Lim_OLIM(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X0,X1),X0,tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_104
| ~ spl0_118 ),
inference(superposition,[],[f1160,f1100]) ).
fof(f1100,plain,
( ! [X21,X9] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X9,X21)) = X9
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1160,plain,
( ! [X1] : c_Lim_OLIM(c_Complex_ORe,X1,hAPP(c_Complex_ORe,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f1625,plain,
( spl0_199
| ~ spl0_100
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1174,f1159,f1081,f1622]) ).
fof(f1622,plain,
( spl0_199
<=> c_Lim_OLIM(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1081,plain,
( spl0_100
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1174,plain,
( c_Lim_OLIM(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_100
| ~ spl0_118 ),
inference(superposition,[],[f1160,f1083]) ).
fof(f1083,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1585,plain,
spl0_198,
inference(avatar_split_clause,[],[f596,f1583]) ).
fof(f1583,plain,
( spl0_198
<=> ! [X9] : c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f596,plain,
! [X9] : c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(forward_demodulation,[],[f458,f294]) ).
fof(f294,axiom,
! [X9] : c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_2) ).
fof(f458,axiom,
! [X9] : hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X9) = hAPP(c_Complex_Ocnj,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__complex__of__real_0) ).
fof(f1581,plain,
spl0_197,
inference(avatar_split_clause,[],[f510,f1579]) ).
fof(f1579,plain,
( spl0_197
<=> ! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f510,axiom,
! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Osummable_0) ).
fof(f1577,plain,
spl0_196,
inference(avatar_split_clause,[],[f500,f1575]) ).
fof(f1575,plain,
( spl0_196
<=> ! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f500,axiom,
! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OCauchy_0) ).
fof(f1573,plain,
spl0_195,
inference(avatar_split_clause,[],[f496,f1571]) ).
fof(f1571,plain,
( spl0_195
<=> ! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f496,axiom,
! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_ORe,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OZseq_0) ).
fof(f1569,plain,
spl0_194,
inference(avatar_split_clause,[],[f459,f1567]) ).
fof(f1567,plain,
( spl0_194
<=> ! [X6,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X6,X0)
| c_Series_Osums(X6,c_Series_Osuminf(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f459,axiom,
! [X0,X6] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X6,X0)
| c_Series_Osums(X6,c_Series_Osuminf(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__sums_0) ).
fof(f1565,plain,
spl0_193,
inference(avatar_split_clause,[],[f454,f1563]) ).
fof(f1563,plain,
( spl0_193
<=> ! [X6,X0,X40] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osums(X6,X40,X0)
| c_Series_Osuminf(X6,X0) = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f454,axiom,
! [X40,X0,X6] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osums(X6,X40,X0)
| c_Series_Osuminf(X6,X0) = X40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__unique_0) ).
fof(f1561,plain,
spl0_192,
inference(avatar_split_clause,[],[f437,f1559]) ).
fof(f1559,plain,
( spl0_192
<=> ! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f437,axiom,
! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OZseq_0) ).
fof(f1557,plain,
spl0_191,
inference(avatar_split_clause,[],[f430,f1555]) ).
fof(f1555,plain,
( spl0_191
<=> ! [X36,X37] :
( X36 = X37
| ~ c_lessequals(X36,X37,tc_nat)
| c_HOL_Oord__class_Oless(X36,X37,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f430,axiom,
! [X36,X37] :
( X36 = X37
| ~ c_lessequals(X36,X37,tc_nat)
| c_HOL_Oord__class_Oless(X36,X37,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
fof(f1553,plain,
spl0_190,
inference(avatar_split_clause,[],[f422,f1551]) ).
fof(f1551,plain,
( spl0_190
<=> ! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f422,axiom,
! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OCauchy_0) ).
fof(f1549,plain,
( ~ spl0_188
| spl0_189
| ~ spl0_103
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1173,f1150,f1095,f1547,f1543]) ).
fof(f1543,plain,
( spl0_188
<=> c_SEQ_Osubseq(c_Complex_Ocnj) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1547,plain,
( spl0_189
<=> ! [X0] : c_lessequals(hAPP(c_Complex_Ocnj,X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1095,plain,
( spl0_103
<=> ! [X22] : hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,X22)) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1150,plain,
( spl0_116
<=> ! [X6,X37] :
( ~ c_SEQ_Osubseq(X6)
| c_lessequals(X37,hAPP(X6,X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1173,plain,
( ! [X0] :
( c_lessequals(hAPP(c_Complex_Ocnj,X0),X0,tc_nat)
| ~ c_SEQ_Osubseq(c_Complex_Ocnj) )
| ~ spl0_103
| ~ spl0_116 ),
inference(superposition,[],[f1151,f1096]) ).
fof(f1096,plain,
( ! [X22] : hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,X22)) = X22
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f1151,plain,
( ! [X37,X6] :
( c_lessequals(X37,hAPP(X6,X37),tc_nat)
| ~ c_SEQ_Osubseq(X6) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f1541,plain,
spl0_187,
inference(avatar_split_clause,[],[f420,f1539]) ).
fof(f1539,plain,
( spl0_187
<=> ! [X9,X21,X23] :
( X9 = X23
| c_Complex_Ocomplex_OComplex(X9,X21) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f420,axiom,
! [X21,X9,X23] :
( X9 = X23
| c_Complex_Ocomplex_OComplex(X9,X21) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_0) ).
fof(f1537,plain,
spl0_186,
inference(avatar_split_clause,[],[f412,f1535]) ).
fof(f1535,plain,
( spl0_186
<=> ! [X36,X37] :
( X36 = X37
| ~ c_lessequals(X36,X37,tc_nat)
| ~ c_lessequals(X37,X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f412,axiom,
! [X36,X37] :
( X36 = X37
| ~ c_lessequals(X36,X37,tc_nat)
| ~ c_lessequals(X37,X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f1533,plain,
spl0_185,
inference(avatar_split_clause,[],[f408,f1531]) ).
fof(f1531,plain,
( spl0_185
<=> ! [X9,X21] :
( X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f408,axiom,
! [X21,X9] :
( X9 = X21
| c_HOL_Oord__class_Oless(X9,X21,tc_nat)
| c_HOL_Oord__class_Oless(X21,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f1529,plain,
spl0_184,
inference(avatar_split_clause,[],[f387,f1527]) ).
fof(f1527,plain,
( spl0_184
<=> ! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f387,axiom,
! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_OIm,X25,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Osummable_0) ).
fof(f1525,plain,
spl0_183,
inference(avatar_split_clause,[],[f373,f1523]) ).
fof(f1523,plain,
( spl0_183
<=> ! [X9,X0] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9)) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f373,axiom,
! [X0,X9] :
( ~ class_Lattices_Oboolean__algebra(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X9)) = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
fof(f1521,plain,
spl0_182,
inference(avatar_split_clause,[],[f370,f1519]) ).
fof(f1519,plain,
( spl0_182
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f370,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
fof(f1517,plain,
spl0_181,
inference(avatar_split_clause,[],[f336,f1515]) ).
fof(f1515,plain,
( spl0_181
<=> ! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f336,axiom,
! [X25] :
( ~ c_Series_Osummable(X25,tc_Complex_Ocomplex)
| c_Series_Osummable(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Osummable_0) ).
fof(f1513,plain,
spl0_180,
inference(avatar_split_clause,[],[f331,f1511]) ).
fof(f1511,plain,
( spl0_180
<=> ! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f331,axiom,
! [X25] :
( ~ c_SEQ_OZseq(X25,tc_Complex_Ocomplex)
| c_SEQ_OZseq(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OZseq_0) ).
fof(f1509,plain,
spl0_179,
inference(avatar_split_clause,[],[f330,f1507]) ).
fof(f1507,plain,
( spl0_179
<=> ! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f330,axiom,
! [X25] :
( ~ c_SEQ_OCauchy(X25,tc_Complex_Ocomplex)
| c_SEQ_OCauchy(c_COMBB(c_Complex_Ocnj,X25,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_OCauchy_0) ).
fof(f1505,plain,
spl0_178,
inference(avatar_split_clause,[],[f235,f1503]) ).
fof(f1503,plain,
( spl0_178
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f235,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f1498,plain,
spl0_177,
inference(avatar_split_clause,[],[f215,f1496]) ).
fof(f1496,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f215,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1494,plain,
spl0_176,
inference(avatar_split_clause,[],[f214,f1492]) ).
fof(f1492,plain,
( spl0_176
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f214,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1490,plain,
spl0_175,
inference(avatar_split_clause,[],[f213,f1488]) ).
fof(f1488,plain,
( spl0_175
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f213,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1486,plain,
spl0_174,
inference(avatar_split_clause,[],[f212,f1484]) ).
fof(f1484,plain,
( spl0_174
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f212,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1482,plain,
spl0_173,
inference(avatar_split_clause,[],[f210,f1480]) ).
fof(f1480,plain,
( spl0_173
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X9,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f210,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X9,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
fof(f1478,plain,
spl0_172,
inference(avatar_split_clause,[],[f208,f1476]) ).
fof(f1476,plain,
( spl0_172
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f208,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f1474,plain,
spl0_171,
inference(avatar_split_clause,[],[f206,f1472]) ).
fof(f1472,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f206,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1470,plain,
spl0_170,
inference(avatar_split_clause,[],[f205,f1468]) ).
fof(f1468,plain,
( spl0_170
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f205,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1466,plain,
spl0_169,
inference(avatar_split_clause,[],[f179,f1464]) ).
fof(f1464,plain,
( spl0_169
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f179,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
fof(f1462,plain,
spl0_168,
inference(avatar_split_clause,[],[f178,f1460]) ).
fof(f1460,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f178,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f1458,plain,
( spl0_167
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1424,f1339,f1456]) ).
fof(f1456,plain,
( spl0_167
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1339,plain,
( spl0_156
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X21,X0)
| c_lessequals(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1424,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_156 ),
inference(factoring,[],[f1340]) ).
fof(f1340,plain,
( ! [X21,X0,X9] :
( c_lessequals(X21,X9,X0)
| c_lessequals(X9,X21,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1339]) ).
fof(f1454,plain,
spl0_166,
inference(avatar_split_clause,[],[f177,f1452]) ).
fof(f1452,plain,
( spl0_166
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f177,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).
fof(f1450,plain,
spl0_165,
inference(avatar_split_clause,[],[f176,f1448]) ).
fof(f1448,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f176,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_OscaleR__class_OscaleR(X1,X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f1446,plain,
spl0_164,
inference(avatar_split_clause,[],[f152,f1444]) ).
fof(f1444,plain,
( spl0_164
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f152,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
fof(f1442,plain,
spl0_163,
inference(avatar_split_clause,[],[f116,f1440]) ).
fof(f1440,plain,
( spl0_163
<=> ! [X22,X26] :
( X22 = X26
| ~ c_lessequals(X22,X26,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X22,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f116,axiom,
! [X26,X22] :
( X22 = X26
| ~ c_lessequals(X22,X26,tc_RealDef_Oreal)
| ~ c_lessequals(X26,X22,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f1438,plain,
spl0_162,
inference(avatar_split_clause,[],[f66,f1436]) ).
fof(f66,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
fof(f1434,plain,
spl0_161,
inference(avatar_split_clause,[],[f58,f1432]) ).
fof(f1432,plain,
( spl0_161
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f58,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f1430,plain,
spl0_160,
inference(avatar_split_clause,[],[f25,f1428]) ).
fof(f1428,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f25,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Otimes__class_Otimes(X1,X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1372,plain,
( ~ spl0_159
| spl0_142
| ~ spl0_101
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1170,f1150,f1086,f1282,f1369]) ).
fof(f1369,plain,
( spl0_159
<=> c_SEQ_Osubseq(c_Complex_OIm) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1282,plain,
( spl0_142
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1086,plain,
( spl0_101
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1170,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_nat)
| ~ c_SEQ_Osubseq(c_Complex_OIm)
| ~ spl0_101
| ~ spl0_116 ),
inference(superposition,[],[f1151,f1088]) ).
fof(f1088,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1349,plain,
spl0_158,
inference(avatar_split_clause,[],[f482,f1347]) ).
fof(f1347,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f482,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f1345,plain,
spl0_157,
inference(avatar_split_clause,[],[f481,f1343]) ).
fof(f1343,plain,
( spl0_157
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f481,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f1341,plain,
spl0_156,
inference(avatar_split_clause,[],[f479,f1339]) ).
fof(f479,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X9,X21,X0)
| c_lessequals(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f1337,plain,
spl0_155,
inference(avatar_split_clause,[],[f477,f1335]) ).
fof(f1335,plain,
( spl0_155
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f477,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f1333,plain,
spl0_154,
inference(avatar_split_clause,[],[f457,f1331]) ).
fof(f1331,plain,
( spl0_154
<=> ! [X9,X21] :
( X9 = X21
| hAPP(c_Complex_Ocnj,X9) != hAPP(c_Complex_Ocnj,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f457,axiom,
! [X21,X9] :
( X9 = X21
| hAPP(c_Complex_Ocnj,X9) != hAPP(c_Complex_Ocnj,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
fof(f1329,plain,
spl0_153,
inference(avatar_split_clause,[],[f452,f1327]) ).
fof(f1327,plain,
( spl0_153
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f452,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f1325,plain,
spl0_152,
inference(avatar_split_clause,[],[f450,f1323]) ).
fof(f1323,plain,
( spl0_152
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f450,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f1321,plain,
spl0_151,
inference(avatar_split_clause,[],[f424,f1319]) ).
fof(f1319,plain,
( spl0_151
<=> ! [X48,X51,X50,X49] :
( X48 = X50
| c_Complex_Ocomplex_OComplex(X48,X49) != c_Complex_Ocomplex_OComplex(X50,X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f424,axiom,
! [X50,X51,X48,X49] :
( X48 = X50
| c_Complex_Ocomplex_OComplex(X48,X49) != c_Complex_Ocomplex_OComplex(X50,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
fof(f1317,plain,
spl0_150,
inference(avatar_split_clause,[],[f423,f1315]) ).
fof(f1315,plain,
( spl0_150
<=> ! [X50,X48,X51,X49] :
( X49 = X51
| c_Complex_Ocomplex_OComplex(X48,X49) != c_Complex_Ocomplex_OComplex(X50,X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f423,axiom,
! [X50,X51,X48,X49] :
( X49 = X51
| c_Complex_Ocomplex_OComplex(X48,X49) != c_Complex_Ocomplex_OComplex(X50,X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
fof(f1313,plain,
spl0_149,
inference(avatar_split_clause,[],[f397,f1311]) ).
fof(f1311,plain,
( spl0_149
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_lessequals(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f397,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X21,X0)
| ~ c_lessequals(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f1309,plain,
spl0_148,
inference(avatar_split_clause,[],[f392,f1307]) ).
fof(f1307,plain,
( spl0_148
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X21,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f392,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X9,X21,X0)
| c_lessequals(X21,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
fof(f1305,plain,
spl0_147,
inference(avatar_split_clause,[],[f390,f1303]) ).
fof(f1303,plain,
( spl0_147
<=> ! [X9,X0,X21] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_lessequals(X9,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f390,axiom,
! [X21,X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X9,X0)
| ~ c_lessequals(X9,X21,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f1301,plain,
spl0_146,
inference(avatar_split_clause,[],[f360,f1299]) ).
fof(f1299,plain,
( spl0_146
<=> ! [X25] :
( c_SEQ_Odecseq(X25)
| ~ c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X25,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f360,axiom,
! [X25] :
( c_SEQ_Odecseq(X25)
| ~ c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X25,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_1) ).
fof(f1297,plain,
spl0_145,
inference(avatar_split_clause,[],[f359,f1295]) ).
fof(f1295,plain,
( spl0_145
<=> ! [X25] :
( ~ c_SEQ_Odecseq(X25)
| c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X25,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f359,axiom,
! [X25] :
( ~ c_SEQ_Odecseq(X25)
| c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X25,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__eq__incseq_0) ).
fof(f1293,plain,
spl0_144,
inference(avatar_split_clause,[],[f285,f1291]) ).
fof(f1291,plain,
( spl0_144
<=> ! [X6,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X6,X0)
| c_SEQ_OLIMSEQ(X6,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f285,axiom,
! [X0,X6] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| ~ c_Series_Osummable(X6,X0)
| c_SEQ_OLIMSEQ(X6,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_summable__LIMSEQ__zero_0) ).
fof(f1289,plain,
spl0_143,
inference(avatar_split_clause,[],[f250,f1287]) ).
fof(f1287,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f250,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
fof(f1285,plain,
( ~ spl0_141
| spl0_142
| ~ spl0_100
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1169,f1150,f1081,f1282,f1278]) ).
fof(f1278,plain,
( spl0_141
<=> c_SEQ_Osubseq(c_Complex_ORe) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1169,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_nat)
| ~ c_SEQ_Osubseq(c_Complex_ORe)
| ~ spl0_100
| ~ spl0_116 ),
inference(superposition,[],[f1151,f1083]) ).
fof(f1276,plain,
spl0_140,
inference(avatar_split_clause,[],[f233,f1274]) ).
fof(f1274,plain,
( spl0_140
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f233,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Complex__eq__0_0) ).
fof(f1272,plain,
spl0_139,
inference(avatar_split_clause,[],[f232,f1270]) ).
fof(f1270,plain,
( spl0_139
<=> ! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f232,axiom,
! [X2,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X2
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Complex_Ocomplex_OComplex(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Complex__eq__0_1) ).
fof(f1268,plain,
spl0_138,
inference(avatar_split_clause,[],[f228,f1266]) ).
fof(f1266,plain,
( spl0_138
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f228,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1264,plain,
spl0_137,
inference(avatar_split_clause,[],[f227,f1262]) ).
fof(f227,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1260,plain,
spl0_136,
inference(avatar_split_clause,[],[f224,f1258]) ).
fof(f1258,plain,
( spl0_136
<=> ! [X1] :
( ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f224,axiom,
! [X1] :
( ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoseq__minus_0) ).
fof(f1256,plain,
spl0_135,
inference(avatar_split_clause,[],[f223,f1254]) ).
fof(f1254,plain,
( spl0_135
<=> ! [X22] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X22
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Complex_Ocnj,X22) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f223,axiom,
! [X22] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X22
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Complex_Ocnj,X22) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
fof(f1252,plain,
spl0_134,
inference(avatar_split_clause,[],[f218,f1250]) ).
fof(f1250,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f218,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X0),X1),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f1248,plain,
spl0_133,
inference(avatar_split_clause,[],[f163,f1246]) ).
fof(f163,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_HOL_Oabs__class_Oabs(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1244,plain,
spl0_132,
inference(avatar_split_clause,[],[f123,f1242]) ).
fof(f123,axiom,
! [X0] :
( ~ class_RealVector_Oreal__algebra__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = hAPP(c_RealVector_Oof__real(X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
fof(f1240,plain,
spl0_131,
inference(avatar_split_clause,[],[f93,f1238]) ).
fof(f93,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealVector_Onorm__class_Onorm(X0),c_HOL_Ozero__class_Ozero(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
fof(f1236,plain,
( spl0_130
| ~ spl0_102
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1166,f1142,f1091,f1234]) ).
fof(f1234,plain,
( spl0_130
<=> ! [X0,X1] : c_Lim_OLIM(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X0,X1),X1,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1091,plain,
( spl0_102
<=> ! [X9,X21] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X9,X21)) = X21 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1142,plain,
( spl0_114
<=> ! [X1] : c_Lim_OLIM(c_Complex_OIm,X1,hAPP(c_Complex_OIm,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f1166,plain,
( ! [X0,X1] : c_Lim_OLIM(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X0,X1),X1,tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_114 ),
inference(superposition,[],[f1143,f1092]) ).
fof(f1092,plain,
( ! [X21,X9] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X9,X21)) = X21
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1143,plain,
( ! [X1] : c_Lim_OLIM(c_Complex_OIm,X1,hAPP(c_Complex_OIm,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1232,plain,
spl0_129,
inference(avatar_split_clause,[],[f48,f1230]) ).
fof(f1230,plain,
( spl0_129
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(X0),X9),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f48,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(X0),X9),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
fof(f1217,plain,
spl0_128,
inference(avatar_split_clause,[],[f489,f1215]) ).
fof(f1215,plain,
( spl0_128
<=> ! [X9] : hAPP(c_Complex_ORe,X9) = hAPP(c_Complex_ORe,hAPP(c_Complex_Ocnj,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f489,axiom,
! [X9] : hAPP(c_Complex_ORe,X9) = hAPP(c_Complex_ORe,hAPP(c_Complex_Ocnj,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__cnj_0) ).
fof(f1213,plain,
( spl0_127
| ~ spl0_101
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1165,f1142,f1086,f1210]) ).
fof(f1210,plain,
( spl0_127
<=> c_Lim_OLIM(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1165,plain,
( c_Lim_OLIM(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Complex_Ocomplex,tc_RealDef_Oreal)
| ~ spl0_101
| ~ spl0_114 ),
inference(superposition,[],[f1143,f1088]) ).
fof(f1208,plain,
spl0_126,
inference(avatar_split_clause,[],[f456,f1206]) ).
fof(f1206,plain,
( spl0_126
<=> ! [X22] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X22),hAPP(c_Complex_OIm,X22)) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f456,axiom,
! [X22] : c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X22),hAPP(c_Complex_OIm,X22)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__surj_0) ).
fof(f1204,plain,
spl0_125,
inference(avatar_split_clause,[],[f441,f1202]) ).
fof(f1202,plain,
( spl0_125
<=> ! [X6,X0,X27] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Series_Osummable(X6,X0)
| ~ c_Series_Osums(X6,X27,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f441,axiom,
! [X0,X6,X27] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Series_Osummable(X6,X0)
| ~ c_Series_Osums(X6,X27,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sums__summable_0) ).
fof(f1200,plain,
spl0_124,
inference(avatar_split_clause,[],[f401,f1198]) ).
fof(f1198,plain,
( spl0_124
<=> ! [X25,X0,X1] :
( ~ class_RealVector_Ometric__space(X0)
| c_SEQ_OCauchy(X25,X0)
| ~ c_SEQ_OLIMSEQ(X25,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f401,axiom,
! [X0,X1,X25] :
( ~ class_RealVector_Ometric__space(X0)
| c_SEQ_OCauchy(X25,X0)
| ~ c_SEQ_OLIMSEQ(X25,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).
fof(f1196,plain,
spl0_123,
inference(avatar_split_clause,[],[f294,f1194]) ).
fof(f1194,plain,
( spl0_123
<=> ! [X9] : c_Complex_Ocomplex_OComplex(X9,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1191,plain,
spl0_122,
inference(avatar_split_clause,[],[f291,f1189]) ).
fof(f1189,plain,
( spl0_122
<=> ! [X22] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f291,axiom,
! [X22] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im__complex__of__real_0) ).
fof(f1187,plain,
spl0_121,
inference(avatar_split_clause,[],[f200,f1185]) ).
fof(f1185,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f200,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_lessequals(X1,hAPP(c_HOL_Oabs__class_Oabs(X0),X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
fof(f1183,plain,
spl0_120,
inference(avatar_split_clause,[],[f127,f1181]) ).
fof(f1181,plain,
( spl0_120
<=> ! [X9,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OisCont(c_HOL_Otimes__class_Otimes(X9,X0),X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f127,axiom,
! [X0,X1,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OisCont(c_HOL_Otimes__class_Otimes(X9,X0),X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).
fof(f1179,plain,
spl0_119,
inference(avatar_split_clause,[],[f86,f1177]) ).
fof(f1177,plain,
( spl0_119
<=> ! [X0,X1,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f86,axiom,
! [X0,X1,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(X8,X0),X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OisCont_0) ).
fof(f1161,plain,
spl0_118,
inference(avatar_split_clause,[],[f498,f1159]) ).
fof(f498,axiom,
! [X1] : c_Lim_OLIM(c_Complex_ORe,X1,hAPP(c_Complex_ORe,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ocont_0) ).
fof(f1156,plain,
spl0_117,
inference(avatar_split_clause,[],[f497,f1154]) ).
fof(f1154,plain,
( spl0_117
<=> ! [X22] : hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X22)) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f497,axiom,
! [X22] : hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X22)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re__complex__of__real_0) ).
fof(f1152,plain,
spl0_116,
inference(avatar_split_clause,[],[f493,f1150]) ).
fof(f493,axiom,
! [X37,X6] :
( ~ c_SEQ_Osubseq(X6)
| c_lessequals(X37,hAPP(X6,X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__suble_0) ).
fof(f1148,plain,
spl0_115,
inference(avatar_split_clause,[],[f480,f1146]) ).
fof(f1146,plain,
( spl0_115
<=> ! [X36,X37] :
( c_lessequals(X36,X37,tc_nat)
| c_lessequals(X37,X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f480,axiom,
! [X36,X37] :
( c_lessequals(X36,X37,tc_nat)
| c_lessequals(X37,X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1144,plain,
spl0_114,
inference(avatar_split_clause,[],[f476,f1142]) ).
fof(f476,axiom,
! [X1] : c_Lim_OLIM(c_Complex_OIm,X1,hAPP(c_Complex_OIm,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ocont_0) ).
fof(f1140,plain,
spl0_113,
inference(avatar_split_clause,[],[f451,f1138]) ).
fof(f1138,plain,
( spl0_113
<=> ! [X36,X37] :
( ~ c_HOL_Oord__class_Oless(X36,X37,tc_nat)
| c_lessequals(X36,X37,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f451,axiom,
! [X36,X37] :
( ~ c_HOL_Oord__class_Oless(X36,X37,tc_nat)
| c_lessequals(X36,X37,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1136,plain,
spl0_112,
inference(avatar_split_clause,[],[f308,f1134]) ).
fof(f1134,plain,
( spl0_112
<=> ! [X40] : c_SEQ_Omonoseq(c_COMBB(X40,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X40),tc_nat,tc_RealDef_Oreal,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f308,axiom,
! [X40] : c_SEQ_Omonoseq(c_COMBB(X40,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X40),tc_nat,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_1) ).
fof(f1132,plain,
spl0_111,
inference(avatar_split_clause,[],[f252,f1130]) ).
fof(f1130,plain,
( spl0_111
<=> ! [X22,X26] :
( c_lessequals(X22,X26,tc_RealDef_Oreal)
| c_lessequals(X26,X22,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f252,axiom,
! [X26,X22] :
( c_lessequals(X22,X26,tc_RealDef_Oreal)
| c_lessequals(X26,X22,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f1128,plain,
spl0_110,
inference(avatar_split_clause,[],[f251,f1126]) ).
fof(f1126,plain,
( spl0_110
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(X1,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f251,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(X1,X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Obounded__linear__right_0) ).
fof(f1124,plain,
spl0_109,
inference(avatar_split_clause,[],[f222,f1122]) ).
fof(f1122,plain,
( spl0_109
<=> ! [X0,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(X8,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f222,axiom,
! [X0,X8] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(X8,X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OisUCont_0) ).
fof(f1120,plain,
spl0_108,
inference(avatar_split_clause,[],[f117,f1118]) ).
fof(f1118,plain,
( spl0_108
<=> ! [X9,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(X9,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f117,axiom,
! [X0,X9] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(X9,X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OisUCont_0) ).
fof(f1116,plain,
spl0_107,
inference(avatar_split_clause,[],[f96,f1113]) ).
fof(f1113,plain,
( spl0_107
<=> c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f96,axiom,
c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__zero__def_0) ).
fof(f1111,plain,
spl0_106,
inference(avatar_split_clause,[],[f19,f1109]) ).
fof(f1109,plain,
( spl0_106
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(X1,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f19,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(X1,X0),X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Obounded__linear__right_0) ).
fof(f1105,plain,
spl0_105,
inference(avatar_split_clause,[],[f595,f1103]) ).
fof(f1103,plain,
( spl0_105
<=> ! [X25,X0,X56] :
( X25 = X56
| ~ c_fequal(X25,X56,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f595,axiom,
! [X0,X56,X25] :
( X25 = X56
| ~ c_fequal(X25,X56,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f1101,plain,
spl0_104,
inference(avatar_split_clause,[],[f483,f1099]) ).
fof(f483,axiom,
! [X21,X9] : hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X9,X21)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_0) ).
fof(f1097,plain,
spl0_103,
inference(avatar_split_clause,[],[f443,f1095]) ).
fof(f443,axiom,
! [X22] : hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,X22)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
fof(f1093,plain,
spl0_102,
inference(avatar_split_clause,[],[f440,f1091]) ).
fof(f440,axiom,
! [X21,X9] : hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X9,X21)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_0) ).
fof(f1089,plain,
spl0_101,
inference(avatar_split_clause,[],[f204,f1086]) ).
fof(f204,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_Ozero_0) ).
fof(f1084,plain,
spl0_100,
inference(avatar_split_clause,[],[f168,f1081]) ).
fof(f168,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_Ozero_0) ).
fof(f1079,plain,
spl0_99,
inference(avatar_split_clause,[],[f160,f1076]) ).
fof(f1076,plain,
( spl0_99
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Complex_Ocnj,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f160,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Complex_Ocnj,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
fof(f1074,plain,
spl0_98,
inference(avatar_split_clause,[],[f516,f1072]) ).
fof(f1072,plain,
( spl0_98
<=> ! [X54,X55] :
( ~ class_Orderings_Oorder(X55)
| class_Orderings_Oorder(tc_fun(X54,X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f516,axiom,
! [X54,X55] :
( ~ class_Orderings_Oorder(X55)
| class_Orderings_Oorder(tc_fun(X54,X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f1070,plain,
spl0_97,
inference(avatar_split_clause,[],[f515,f1068]) ).
fof(f1068,plain,
( spl0_97
<=> ! [X54,X55] :
( ~ class_Orderings_Opreorder(X55)
| class_Orderings_Opreorder(tc_fun(X54,X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f515,axiom,
! [X54,X55] :
( ~ class_Orderings_Opreorder(X55)
| class_Orderings_Opreorder(tc_fun(X54,X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f1066,plain,
spl0_96,
inference(avatar_split_clause,[],[f514,f1064]) ).
fof(f1064,plain,
( spl0_96
<=> ! [X54,X55] :
( ~ class_Lattices_Oboolean__algebra(X55)
| class_Lattices_Oboolean__algebra(tc_fun(X54,X55)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f514,axiom,
! [X54,X55] :
( ~ class_Lattices_Oboolean__algebra(X55)
| class_Lattices_Oboolean__algebra(tc_fun(X54,X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
fof(f1062,plain,
spl0_95,
inference(avatar_split_clause,[],[f462,f1060]) ).
fof(f1060,plain,
( spl0_95
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f462,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1058,plain,
spl0_94,
inference(avatar_split_clause,[],[f461,f1056]) ).
fof(f1056,plain,
( spl0_94
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f461,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1054,plain,
spl0_93,
inference(avatar_split_clause,[],[f448,f1052]) ).
fof(f1052,plain,
( spl0_93
<=> ! [X9,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f448,axiom,
! [X0,X9] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1050,plain,
spl0_92,
inference(avatar_split_clause,[],[f445,f1048]) ).
fof(f1048,plain,
( spl0_92
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f445,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1046,plain,
spl0_91,
inference(avatar_split_clause,[],[f444,f1044]) ).
fof(f1044,plain,
( spl0_91
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f444,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1042,plain,
spl0_90,
inference(avatar_split_clause,[],[f506,f1040]) ).
fof(f1040,plain,
( spl0_90
<=> ! [X1] : c_Lim_OisCont(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f506,axiom,
! [X1] : c_Lim_OisCont(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisCont_0) ).
fof(f1038,plain,
spl0_89,
inference(avatar_split_clause,[],[f403,f1036]) ).
fof(f1036,plain,
( spl0_89
<=> ! [X1] : c_Lim_OisCont(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f403,axiom,
! [X1] : c_Lim_OisCont(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisCont_0) ).
fof(f1034,plain,
spl0_88,
inference(avatar_split_clause,[],[f594,f1032]) ).
fof(f1032,plain,
( spl0_88
<=> ! [X9,X0] : c_fequal(X9,X9,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f594,axiom,
! [X0,X9] : c_fequal(X9,X9,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f1030,plain,
spl0_87,
inference(avatar_split_clause,[],[f503,f1028]) ).
fof(f1028,plain,
( spl0_87
<=> ! [X25] :
( ~ c_SEQ_Odecseq(X25)
| c_SEQ_Omonoseq(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f503,axiom,
! [X25] :
( ~ c_SEQ_Odecseq(X25)
| c_SEQ_Omonoseq(X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_decseq__imp__monoseq_0) ).
fof(f1026,plain,
spl0_86,
inference(avatar_split_clause,[],[f487,f1024]) ).
fof(f1024,plain,
( spl0_86
<=> ! [X25] :
( ~ c_SEQ_Oincseq(X25)
| c_SEQ_Omonoseq(X25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f487,axiom,
! [X25] :
( ~ c_SEQ_Oincseq(X25)
| c_SEQ_Omonoseq(X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_incseq__imp__monoseq_0) ).
fof(f1022,plain,
spl0_85,
inference(avatar_split_clause,[],[f484,f1019]) ).
fof(f1019,plain,
( spl0_85
<=> c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f484,axiom,
c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Re_OisUCont_0) ).
fof(f1017,plain,
spl0_84,
inference(avatar_split_clause,[],[f475,f1014]) ).
fof(f1014,plain,
( spl0_84
<=> c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f475,axiom,
c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Im_OisUCont_0) ).
fof(f1012,plain,
spl0_83,
inference(avatar_split_clause,[],[f463,f1010]) ).
fof(f1010,plain,
( spl0_83
<=> ! [X9] : c_lessequals(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f463,axiom,
! [X9] : c_lessequals(X9,X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
fof(f1008,plain,
spl0_82,
inference(avatar_split_clause,[],[f447,f1006]) ).
fof(f1006,plain,
( spl0_82
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f447,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f1004,plain,
spl0_81,
inference(avatar_split_clause,[],[f237,f1002]) ).
fof(f1002,plain,
( spl0_81
<=> ! [X26] : c_lessequals(X26,X26,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f237,axiom,
! [X26] : c_lessequals(X26,X26,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f1000,plain,
spl0_80,
inference(avatar_split_clause,[],[f512,f997]) ).
fof(f512,axiom,
c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f995,plain,
spl0_79,
inference(avatar_split_clause,[],[f488,f993]) ).
fof(f993,plain,
( spl0_79
<=> ! [X40] : c_SEQ_Osubseq(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X40)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f488,axiom,
! [X40] : c_SEQ_Osubseq(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_seq__monosub_0) ).
fof(f991,plain,
spl0_78,
inference(avatar_split_clause,[],[f593,f988]) ).
fof(f988,plain,
( spl0_78
<=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f593,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
fof(f986,plain,
spl0_77,
inference(avatar_split_clause,[],[f592,f983]) ).
fof(f983,plain,
( spl0_77
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f592,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f981,plain,
spl0_76,
inference(avatar_split_clause,[],[f591,f978]) ).
fof(f978,plain,
( spl0_76
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f591,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f976,plain,
spl0_75,
inference(avatar_split_clause,[],[f590,f973]) ).
fof(f590,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f971,plain,
spl0_74,
inference(avatar_split_clause,[],[f589,f968]) ).
fof(f968,plain,
( spl0_74
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f589,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
fof(f966,plain,
spl0_73,
inference(avatar_split_clause,[],[f588,f963]) ).
fof(f963,plain,
( spl0_73
<=> class_RealVector_Ometric__space(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f588,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
fof(f961,plain,
spl0_72,
inference(avatar_split_clause,[],[f587,f958]) ).
fof(f958,plain,
( spl0_72
<=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f587,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
fof(f956,plain,
spl0_71,
inference(avatar_split_clause,[],[f586,f953]) ).
fof(f953,plain,
( spl0_71
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f586,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(f951,plain,
spl0_70,
inference(avatar_split_clause,[],[f585,f948]) ).
fof(f948,plain,
( spl0_70
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f585,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f946,plain,
spl0_69,
inference(avatar_split_clause,[],[f584,f943]) ).
fof(f584,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(f941,plain,
spl0_68,
inference(avatar_split_clause,[],[f583,f938]) ).
fof(f938,plain,
( spl0_68
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f583,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(f936,plain,
spl0_67,
inference(avatar_split_clause,[],[f582,f933]) ).
fof(f933,plain,
( spl0_67
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f582,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f931,plain,
spl0_66,
inference(avatar_split_clause,[],[f581,f928]) ).
fof(f581,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f926,plain,
spl0_65,
inference(avatar_split_clause,[],[f580,f923]) ).
fof(f923,plain,
( spl0_65
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f580,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f921,plain,
spl0_64,
inference(avatar_split_clause,[],[f579,f918]) ).
fof(f918,plain,
( spl0_64
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f579,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f916,plain,
spl0_63,
inference(avatar_split_clause,[],[f578,f913]) ).
fof(f913,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f578,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(f911,plain,
spl0_62,
inference(avatar_split_clause,[],[f577,f908]) ).
fof(f908,plain,
( spl0_62
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f577,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(f906,plain,
spl0_61,
inference(avatar_split_clause,[],[f576,f903]) ).
fof(f903,plain,
( spl0_61
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f576,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(f901,plain,
spl0_60,
inference(avatar_split_clause,[],[f575,f898]) ).
fof(f898,plain,
( spl0_60
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f575,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(f896,plain,
spl0_59,
inference(avatar_split_clause,[],[f574,f893]) ).
fof(f893,plain,
( spl0_59
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f574,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f891,plain,
spl0_58,
inference(avatar_split_clause,[],[f573,f888]) ).
fof(f888,plain,
( spl0_58
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f573,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f886,plain,
spl0_57,
inference(avatar_split_clause,[],[f572,f883]) ).
fof(f883,plain,
( spl0_57
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f572,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f881,plain,
spl0_56,
inference(avatar_split_clause,[],[f571,f878]) ).
fof(f878,plain,
( spl0_56
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f571,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f876,plain,
spl0_55,
inference(avatar_split_clause,[],[f570,f873]) ).
fof(f873,plain,
( spl0_55
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f570,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f871,plain,
spl0_54,
inference(avatar_split_clause,[],[f569,f868]) ).
fof(f868,plain,
( spl0_54
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f569,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f866,plain,
spl0_53,
inference(avatar_split_clause,[],[f568,f863]) ).
fof(f863,plain,
( spl0_53
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f568,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(f861,plain,
spl0_52,
inference(avatar_split_clause,[],[f567,f858]) ).
fof(f567,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f856,plain,
spl0_51,
inference(avatar_split_clause,[],[f566,f853]) ).
fof(f853,plain,
( spl0_51
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f566,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f851,plain,
spl0_50,
inference(avatar_split_clause,[],[f565,f848]) ).
fof(f848,plain,
( spl0_50
<=> class_RealVector_Ometric__space(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f565,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
fof(f846,plain,
spl0_49,
inference(avatar_split_clause,[],[f564,f843]) ).
fof(f843,plain,
( spl0_49
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f564,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f841,plain,
spl0_48,
inference(avatar_split_clause,[],[f563,f838]) ).
fof(f838,plain,
( spl0_48
<=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f563,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(f836,plain,
spl0_47,
inference(avatar_split_clause,[],[f562,f833]) ).
fof(f833,plain,
( spl0_47
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f562,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(f831,plain,
spl0_46,
inference(avatar_split_clause,[],[f561,f828]) ).
fof(f828,plain,
( spl0_46
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f561,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f826,plain,
spl0_45,
inference(avatar_split_clause,[],[f560,f823]) ).
fof(f560,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(f821,plain,
spl0_44,
inference(avatar_split_clause,[],[f559,f818]) ).
fof(f818,plain,
( spl0_44
<=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f559,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(f816,plain,
spl0_43,
inference(avatar_split_clause,[],[f558,f813]) ).
fof(f813,plain,
( spl0_43
<=> class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f558,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
fof(f811,plain,
spl0_42,
inference(avatar_split_clause,[],[f557,f808]) ).
fof(f808,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f557,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(f806,plain,
spl0_41,
inference(avatar_split_clause,[],[f556,f803]) ).
fof(f803,plain,
( spl0_41
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f556,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f801,plain,
spl0_40,
inference(avatar_split_clause,[],[f555,f798]) ).
fof(f798,plain,
( spl0_40
<=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f555,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(f796,plain,
spl0_39,
inference(avatar_split_clause,[],[f554,f793]) ).
fof(f793,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f554,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(f791,plain,
spl0_38,
inference(avatar_split_clause,[],[f553,f788]) ).
fof(f553,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f786,plain,
spl0_37,
inference(avatar_split_clause,[],[f552,f783]) ).
fof(f783,plain,
( spl0_37
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f552,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f781,plain,
spl0_36,
inference(avatar_split_clause,[],[f551,f778]) ).
fof(f778,plain,
( spl0_36
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f551,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f776,plain,
spl0_35,
inference(avatar_split_clause,[],[f550,f773]) ).
fof(f773,plain,
( spl0_35
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f550,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(f771,plain,
spl0_34,
inference(avatar_split_clause,[],[f549,f768]) ).
fof(f768,plain,
( spl0_34
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f549,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(f766,plain,
spl0_33,
inference(avatar_split_clause,[],[f548,f763]) ).
fof(f763,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f548,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(f761,plain,
spl0_32,
inference(avatar_split_clause,[],[f547,f758]) ).
fof(f758,plain,
( spl0_32
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f547,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(f756,plain,
spl0_31,
inference(avatar_split_clause,[],[f546,f753]) ).
fof(f753,plain,
( spl0_31
<=> class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f546,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(f751,plain,
spl0_30,
inference(avatar_split_clause,[],[f545,f748]) ).
fof(f748,plain,
( spl0_30
<=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f545,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(f746,plain,
spl0_29,
inference(avatar_split_clause,[],[f544,f743]) ).
fof(f743,plain,
( spl0_29
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f544,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f741,plain,
spl0_28,
inference(avatar_split_clause,[],[f543,f738]) ).
fof(f738,plain,
( spl0_28
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f543,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f736,plain,
spl0_27,
inference(avatar_split_clause,[],[f542,f733]) ).
fof(f733,plain,
( spl0_27
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f542,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f731,plain,
spl0_26,
inference(avatar_split_clause,[],[f541,f728]) ).
fof(f728,plain,
( spl0_26
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f541,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(f726,plain,
spl0_25,
inference(avatar_split_clause,[],[f540,f723]) ).
fof(f723,plain,
( spl0_25
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f540,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(f721,plain,
spl0_24,
inference(avatar_split_clause,[],[f539,f718]) ).
fof(f718,plain,
( spl0_24
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f539,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(f716,plain,
spl0_23,
inference(avatar_split_clause,[],[f538,f713]) ).
fof(f538,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(f711,plain,
spl0_22,
inference(avatar_split_clause,[],[f537,f708]) ).
fof(f708,plain,
( spl0_22
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f537,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(f706,plain,
spl0_21,
inference(avatar_split_clause,[],[f536,f703]) ).
fof(f703,plain,
( spl0_21
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f536,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(f701,plain,
spl0_20,
inference(avatar_split_clause,[],[f535,f698]) ).
fof(f698,plain,
( spl0_20
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f535,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(f696,plain,
spl0_19,
inference(avatar_split_clause,[],[f534,f693]) ).
fof(f693,plain,
( spl0_19
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f534,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f691,plain,
spl0_18,
inference(avatar_split_clause,[],[f533,f688]) ).
fof(f688,plain,
( spl0_18
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f533,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f686,plain,
spl0_17,
inference(avatar_split_clause,[],[f532,f683]) ).
fof(f683,plain,
( spl0_17
<=> class_Lattices_Oboolean__algebra(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f532,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
fof(f681,plain,
spl0_16,
inference(avatar_split_clause,[],[f531,f678]) ).
fof(f678,plain,
( spl0_16
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f531,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f676,plain,
spl0_15,
inference(avatar_split_clause,[],[f530,f673]) ).
fof(f673,plain,
( spl0_15
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f530,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f671,plain,
spl0_14,
inference(avatar_split_clause,[],[f529,f668]) ).
fof(f668,plain,
( spl0_14
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f529,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f666,plain,
spl0_13,
inference(avatar_split_clause,[],[f528,f663]) ).
fof(f663,plain,
( spl0_13
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f528,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f661,plain,
spl0_12,
inference(avatar_split_clause,[],[f527,f658]) ).
fof(f658,plain,
( spl0_12
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f527,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f656,plain,
spl0_11,
inference(avatar_split_clause,[],[f526,f653]) ).
fof(f653,plain,
( spl0_11
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f526,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f651,plain,
spl0_10,
inference(avatar_split_clause,[],[f525,f648]) ).
fof(f648,plain,
( spl0_10
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f525,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f646,plain,
spl0_9,
inference(avatar_split_clause,[],[f524,f643]) ).
fof(f643,plain,
( spl0_9
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f524,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f641,plain,
spl0_8,
inference(avatar_split_clause,[],[f523,f638]) ).
fof(f638,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f523,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(f636,plain,
spl0_7,
inference(avatar_split_clause,[],[f522,f633]) ).
fof(f633,plain,
( spl0_7
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f522,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(f631,plain,
spl0_6,
inference(avatar_split_clause,[],[f521,f628]) ).
fof(f628,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f521,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f626,plain,
spl0_5,
inference(avatar_split_clause,[],[f520,f623]) ).
fof(f623,plain,
( spl0_5
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f520,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f621,plain,
spl0_4,
inference(avatar_split_clause,[],[f519,f618]) ).
fof(f618,plain,
( spl0_4
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f519,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(f616,plain,
spl0_3,
inference(avatar_split_clause,[],[f518,f613]) ).
fof(f613,plain,
( spl0_3
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f518,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(f611,plain,
spl0_2,
inference(avatar_split_clause,[],[f517,f608]) ).
fof(f608,plain,
( spl0_2
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f517,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(f606,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f513,f603]) ).
fof(f513,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG361-1 : TPTP v8.2.0. Released v4.1.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n024.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sat May 18 23:40:53 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.32 % (16279)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.36 % (16282)WARNING: value z3 for option sas not known
% 0.10/0.36 % (16282)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)
% 0.10/0.36 % (16283)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.36 % (16281)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.36 % (16284)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)
% 0.10/0.36 % (16280)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.36 % (16285)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)
% 0.10/0.36 % (16286)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)
% 0.16/0.43 TRYING [1]
% 0.16/0.44 TRYING [2]
% 0.16/0.44 % (16284)First to succeed.
% 0.16/0.45 % (16284)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16279"
% 0.16/0.46 % (16284)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (16284)------------------------------
% 0.16/0.46 % (16284)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.46 % (16284)Termination reason: Refutation
% 0.16/0.46
% 0.16/0.46 % (16284)Memory used [KB]: 2664
% 0.16/0.46 % (16284)Time elapsed: 0.097 s
% 0.16/0.46 % (16284)Instructions burned: 175 (million)
% 0.16/0.46 % (16279)Success in time 0.138 s
%------------------------------------------------------------------------------