TSTP Solution File: ALG417-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG417-1 : 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 : n021.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 18:37:40 EDT 2024
% Result : Unsatisfiable 0.23s 0.46s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 550
% Syntax : Number of formulae : 896 ( 367 unt; 0 def)
% Number of atoms : 1768 ( 336 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1468 ( 596 ~; 589 |; 0 &)
% ( 283 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 339 ( 337 usr; 284 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 5 con; 0-3 aty)
% Number of variables : 708 ( 708 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2175,plain,
$false,
inference(avatar_sat_refutation,[],[f547,f552,f556,f562,f567,f572,f577,f582,f587,f592,f597,f602,f607,f612,f617,f622,f627,f632,f637,f642,f647,f652,f657,f662,f667,f672,f677,f682,f687,f692,f697,f702,f707,f712,f717,f722,f727,f732,f737,f742,f747,f752,f757,f762,f767,f772,f777,f782,f787,f792,f797,f802,f807,f812,f817,f822,f827,f832,f837,f842,f847,f852,f857,f862,f867,f872,f877,f882,f887,f892,f897,f902,f907,f912,f917,f922,f927,f932,f937,f942,f947,f952,f957,f962,f967,f972,f977,f982,f987,f992,f997,f1002,f1007,f1012,f1017,f1022,f1027,f1032,f1036,f1040,f1044,f1048,f1052,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1105,f1109,f1113,f1117,f1121,f1125,f1129,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1191,f1196,f1200,f1204,f1209,f1213,f1217,f1223,f1228,f1233,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1391,f1437,f1473,f1489,f1493,f1497,f1501,f1505,f1509,f1513,f1517,f1521,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1558,f1562,f1615,f1619,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1737,f1775,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1905,f1940,f1951,f1955,f1959,f1965,f1969,f1973,f1977,f1981,f1985,f1989,f1993,f1997,f2001,f2009,f2013,f2017,f2021,f2025,f2029,f2033,f2037,f2041,f2045,f2049,f2053,f2057,f2061,f2174]) ).
fof(f2174,plain,
( spl0_98
| ~ spl0_1
| ~ spl0_95
| ~ spl0_146
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2154,f2019,f1230,f1014,f544,f1029]) ).
fof(f1029,plain,
( spl0_98
<=> v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f544,plain,
( spl0_1
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_k____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1014,plain,
( spl0_95
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1230,plain,
( spl0_146
<=> v_s____ = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2019,plain,
( spl0_273
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2154,plain,
( v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl0_1
| ~ spl0_95
| ~ spl0_146
| ~ spl0_273 ),
inference(forward_demodulation,[],[f2153,f1232]) ).
fof(f1232,plain,
( v_s____ = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f2153,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_95
| ~ spl0_273 ),
inference(forward_demodulation,[],[f2151,f546]) ).
fof(f546,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_k____
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f2151,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_95
| ~ spl0_273 ),
inference(resolution,[],[f2020,f1016]) ).
fof(f1016,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f2020,plain,
( ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2019]) ).
fof(f2061,plain,
spl0_283,
inference(avatar_split_clause,[],[f375,f2059]) ).
fof(f2059,plain,
( spl0_283
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f375,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f2057,plain,
spl0_282,
inference(avatar_split_clause,[],[f366,f2055]) ).
fof(f2055,plain,
( spl0_282
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f366,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f2053,plain,
spl0_281,
inference(avatar_split_clause,[],[f358,f2051]) ).
fof(f2051,plain,
( spl0_281
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f358,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f2049,plain,
spl0_280,
inference(avatar_split_clause,[],[f328,f2047]) ).
fof(f2047,plain,
( spl0_280
<=> ! [X6,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f328,axiom,
! [X0,X1,X6] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
fof(f2045,plain,
spl0_279,
inference(avatar_split_clause,[],[f323,f2043]) ).
fof(f2043,plain,
( spl0_279
<=> ! [X0,X19,X31] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X31,X19,X0)
| c_HOL_Oabs__class_Oabs(X19,X0) != c_HOL_Oabs__class_Oabs(X31,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f323,axiom,
! [X31,X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X31,X19,X0)
| c_HOL_Oabs__class_Oabs(X19,X0) != c_HOL_Oabs__class_Oabs(X31,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
fof(f2041,plain,
spl0_278,
inference(avatar_split_clause,[],[f302,f2039]) ).
fof(f2039,plain,
( spl0_278
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X6,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f302,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X6,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f2037,plain,
spl0_277,
inference(avatar_split_clause,[],[f296,f2035]) ).
fof(f2035,plain,
( spl0_277
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f296,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X6,X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f2033,plain,
spl0_276,
inference(avatar_split_clause,[],[f295,f2031]) ).
fof(f2031,plain,
( spl0_276
<=> ! [X5,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X3,X5,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f295,axiom,
! [X3,X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X3,X5,X0),X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f2029,plain,
spl0_275,
inference(avatar_split_clause,[],[f246,f2027]) ).
fof(f2027,plain,
( spl0_275
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f246,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f2025,plain,
spl0_274,
inference(avatar_split_clause,[],[f241,f2023]) ).
fof(f2023,plain,
( spl0_274
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f241,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__neg_0) ).
fof(f2021,plain,
spl0_273,
inference(avatar_split_clause,[],[f227,f2019]) ).
fof(f227,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
fof(f2017,plain,
spl0_272,
inference(avatar_split_clause,[],[f226,f2015]) ).
fof(f2015,plain,
( spl0_272
<=> ! [X6,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X6,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f226,axiom,
! [X0,X1,X6] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X6,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
fof(f2013,plain,
spl0_271,
inference(avatar_split_clause,[],[f225,f2011]) ).
fof(f2011,plain,
( spl0_271
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X6,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f225,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X6,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f2009,plain,
spl0_270,
inference(avatar_split_clause,[],[f211,f2007]) ).
fof(f2007,plain,
( spl0_270
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X6,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f211,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X6,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f2001,plain,
spl0_269,
inference(avatar_split_clause,[],[f173,f1999]) ).
fof(f1999,plain,
( spl0_269
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f173,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).
fof(f1997,plain,
spl0_268,
inference(avatar_split_clause,[],[f125,f1995]) ).
fof(f1995,plain,
( spl0_268
<=> ! [X6,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X6,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f125,axiom,
! [X0,X1,X6] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X6,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
fof(f1993,plain,
spl0_267,
inference(avatar_split_clause,[],[f107,f1991]) ).
fof(f1991,plain,
( spl0_267
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f107,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,X6,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f1989,plain,
spl0_266,
inference(avatar_split_clause,[],[f106,f1987]) ).
fof(f1987,plain,
( spl0_266
<=> ! [X2,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f106,axiom,
! [X2,X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f1985,plain,
spl0_265,
inference(avatar_split_clause,[],[f105,f1983]) ).
fof(f1983,plain,
( spl0_265
<=> ! [X2,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f105,axiom,
! [X2,X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X3,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__def_0) ).
fof(f1981,plain,
spl0_264,
inference(avatar_split_clause,[],[f94,f1979]) ).
fof(f1979,plain,
( spl0_264
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f94,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__neg_0) ).
fof(f1977,plain,
spl0_263,
inference(avatar_split_clause,[],[f57,f1975]) ).
fof(f1975,plain,
( spl0_263
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f57,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f1973,plain,
spl0_262,
inference(avatar_split_clause,[],[f33,f1971]) ).
fof(f1971,plain,
( spl0_262
<=> ! [X6,X0,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X6,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f33,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X6,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f1969,plain,
spl0_261,
inference(avatar_split_clause,[],[f32,f1967]) ).
fof(f1967,plain,
( spl0_261
<=> ! [X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X6,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f32,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X7,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X6,X0),X7,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f1965,plain,
spl0_260,
inference(avatar_split_clause,[],[f31,f1963]) ).
fof(f1963,plain,
( spl0_260
<=> ! [X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f31,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X6,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f1959,plain,
spl0_259,
inference(avatar_split_clause,[],[f30,f1957]) ).
fof(f1957,plain,
( spl0_259
<=> ! [X0,X6,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f30,axiom,
! [X0,X1,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X7,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X7,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f1955,plain,
spl0_258,
inference(avatar_split_clause,[],[f29,f1953]) ).
fof(f1953,plain,
( spl0_258
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X6,X0),X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f29,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X6,X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f1951,plain,
spl0_257,
inference(avatar_split_clause,[],[f6,f1949]) ).
fof(f1949,plain,
( spl0_257
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f6,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__minus_0) ).
fof(f1940,plain,
( spl0_256
| ~ spl0_1
| ~ spl0_88
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f1608,f1547,f979,f544,f1938]) ).
fof(f1938,plain,
( spl0_256
<=> ! [X0] : v_k____ = c_HOL_Oinverse__class_Odivide(v_k____,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f979,plain,
( spl0_88
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1547,plain,
( spl0_201
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1608,plain,
( ! [X0] : v_k____ = c_HOL_Oinverse__class_Odivide(v_k____,X0,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_88
| ~ spl0_201 ),
inference(forward_demodulation,[],[f1607,f546]) ).
fof(f1607,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_88
| ~ spl0_201 ),
inference(resolution,[],[f1548,f981]) ).
fof(f981,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f979]) ).
fof(f1548,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1547]) ).
fof(f1905,plain,
( spl0_255
| ~ spl0_1
| ~ spl0_67
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1602,f1539,f874,f544,f1903]) ).
fof(f1903,plain,
( spl0_255
<=> ! [X0] : v_k____ = c_RealVector_OscaleR__class_OscaleR(X0,v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f874,plain,
( spl0_67
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1539,plain,
( spl0_199
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1602,plain,
( ! [X0] : v_k____ = c_RealVector_OscaleR__class_OscaleR(X0,v_k____,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_67
| ~ spl0_199 ),
inference(forward_demodulation,[],[f1601,f546]) ).
fof(f1601,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_67
| ~ spl0_199 ),
inference(resolution,[],[f1540,f876]) ).
fof(f876,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f1540,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1539]) ).
fof(f1879,plain,
spl0_254,
inference(avatar_split_clause,[],[f398,f1877]) ).
fof(f1877,plain,
( spl0_254
<=> ! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Osgn__class_Osgn(X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f398,axiom,
! [X2,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Osgn__class_Osgn(X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
fof(f1875,plain,
spl0_253,
inference(avatar_split_clause,[],[f397,f1873]) ).
fof(f1873,plain,
( spl0_253
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f397,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
fof(f1871,plain,
spl0_252,
inference(avatar_split_clause,[],[f394,f1869]) ).
fof(f1869,plain,
( spl0_252
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f394,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X6,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).
fof(f1867,plain,
spl0_251,
inference(avatar_split_clause,[],[f391,f1865]) ).
fof(f1865,plain,
( spl0_251
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f391,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f1863,plain,
( spl0_250
| ~ spl0_1
| ~ spl0_57
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1574,f1499,f824,f544,f1861]) ).
fof(f1861,plain,
( spl0_250
<=> ! [X0] : v_k____ = c_HOL_Otimes__class_Otimes(v_k____,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f824,plain,
( spl0_57
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1499,plain,
( spl0_189
<=> ! [X6,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1574,plain,
( ! [X0] : v_k____ = c_HOL_Otimes__class_Otimes(v_k____,X0,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_57
| ~ spl0_189 ),
inference(forward_demodulation,[],[f1572,f546]) ).
fof(f1572,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_57
| ~ spl0_189 ),
inference(resolution,[],[f1500,f826]) ).
fof(f826,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f824]) ).
fof(f1500,plain,
( ! [X0,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1499]) ).
fof(f1859,plain,
spl0_249,
inference(avatar_split_clause,[],[f390,f1857]) ).
fof(f1857,plain,
( spl0_249
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f390,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X6
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f1855,plain,
spl0_248,
inference(avatar_split_clause,[],[f368,f1853]) ).
fof(f1853,plain,
( spl0_248
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f368,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f1851,plain,
spl0_247,
inference(avatar_split_clause,[],[f335,f1849]) ).
fof(f1849,plain,
( spl0_247
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f335,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oinverse__class_Oinverse(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f1847,plain,
spl0_246,
inference(avatar_split_clause,[],[f329,f1845]) ).
fof(f1845,plain,
( spl0_246
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f329,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f1843,plain,
spl0_245,
inference(avatar_split_clause,[],[f310,f1841]) ).
fof(f1841,plain,
( spl0_245
<=> ! [X6,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f310,axiom,
! [X0,X1,X6] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X6,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f1839,plain,
spl0_244,
inference(avatar_split_clause,[],[f309,f1837]) ).
fof(f1837,plain,
( spl0_244
<=> ! [X6,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X1,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f309,axiom,
! [X0,X1,X6] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X6,X1,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f1835,plain,
spl0_243,
inference(avatar_split_clause,[],[f293,f1833]) ).
fof(f1833,plain,
( spl0_243
<=> ! [X25,X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,c_HOL_Oabs__class_Oabs(X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f293,axiom,
! [X0,X19,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,c_HOL_Oabs__class_Oabs(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f1831,plain,
spl0_242,
inference(avatar_split_clause,[],[f292,f1829]) ).
fof(f1829,plain,
( spl0_242
<=> ! [X25,X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_HOL_Oabs__class_Oabs(X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f292,axiom,
! [X0,X19,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,c_HOL_Oabs__class_Oabs(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f1827,plain,
spl0_241,
inference(avatar_split_clause,[],[f291,f1825]) ).
fof(f1825,plain,
( spl0_241
<=> ! [X25,X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X25,X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f291,axiom,
! [X0,X19,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X25,X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f1823,plain,
spl0_240,
inference(avatar_split_clause,[],[f290,f1821]) ).
fof(f1821,plain,
( spl0_240
<=> ! [X25,X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X25,X0),X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f290,axiom,
! [X0,X19,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X25,X19,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X25,X0),X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f1819,plain,
( spl0_239
| ~ spl0_1
| ~ spl0_57
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1570,f1495,f824,f544,f1817]) ).
fof(f1817,plain,
( spl0_239
<=> ! [X0] : v_k____ = c_HOL_Otimes__class_Otimes(X0,v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1495,plain,
( spl0_188
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1570,plain,
( ! [X0] : v_k____ = c_HOL_Otimes__class_Otimes(X0,v_k____,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_57
| ~ spl0_188 ),
inference(forward_demodulation,[],[f1568,f546]) ).
fof(f1568,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_57
| ~ spl0_188 ),
inference(resolution,[],[f1496,f826]) ).
fof(f1496,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1495]) ).
fof(f1815,plain,
spl0_238,
inference(avatar_split_clause,[],[f263,f1813]) ).
fof(f1813,plain,
( spl0_238
<=> ! [X6,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f263,axiom,
! [X0,X1,X6] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X6,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f1811,plain,
spl0_237,
inference(avatar_split_clause,[],[f132,f1809]) ).
fof(f1809,plain,
( spl0_237
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f132,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X2,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
fof(f1807,plain,
spl0_236,
inference(avatar_split_clause,[],[f115,f1805]) ).
fof(f1805,plain,
( spl0_236
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f115,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f1803,plain,
spl0_235,
inference(avatar_split_clause,[],[f114,f1801]) ).
fof(f1801,plain,
( spl0_235
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f114,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f1799,plain,
spl0_234,
inference(avatar_split_clause,[],[f113,f1797]) ).
fof(f1797,plain,
( spl0_234
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f113,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f1795,plain,
spl0_233,
inference(avatar_split_clause,[],[f112,f1793]) ).
fof(f1793,plain,
( spl0_233
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f112,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f1791,plain,
spl0_232,
inference(avatar_split_clause,[],[f99,f1789]) ).
fof(f1789,plain,
( spl0_232
<=> ! [X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X19,X0) = c_HOL_Otimes__class_Otimes(X19,c_HOL_Osgn__class_Osgn(X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f99,axiom,
! [X0,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X19,X0) = c_HOL_Otimes__class_Otimes(X19,c_HOL_Osgn__class_Osgn(X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
fof(f1787,plain,
spl0_231,
inference(avatar_split_clause,[],[f38,f1785]) ).
fof(f1785,plain,
( spl0_231
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f38,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_prts_0) ).
fof(f1783,plain,
spl0_230,
inference(avatar_split_clause,[],[f17,f1781]) ).
fof(f1781,plain,
( spl0_230
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X6
| c_HOL_Ouminus__class_Ouminus(X6,X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f17,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X6
| c_HOL_Ouminus__class_Ouminus(X6,X0) != c_HOL_Ouminus__class_Ouminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f1775,plain,
( spl0_229
| ~ spl0_1
| ~ spl0_83
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1464,f1364,f954,f544,f1773]) ).
fof(f1773,plain,
( spl0_229
<=> ! [X0] : c_HOL_Oplus__class_Oplus(v_k____,X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f954,plain,
( spl0_83
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1364,plain,
( spl0_178
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1464,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(v_k____,X0,tc_Complex_Ocomplex) = X0
| ~ spl0_1
| ~ spl0_83
| ~ spl0_178 ),
inference(forward_demodulation,[],[f1462,f546]) ).
fof(f1462,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_83
| ~ spl0_178 ),
inference(resolution,[],[f1365,f956]) ).
fof(f956,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f1365,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1737,plain,
( spl0_228
| ~ spl0_1
| ~ spl0_83
| ~ spl0_177 ),
inference(avatar_split_clause,[],[f1460,f1360,f954,f544,f1735]) ).
fof(f1735,plain,
( spl0_228
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,v_k____,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1360,plain,
( spl0_177
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1460,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,v_k____,tc_Complex_Ocomplex) = X0
| ~ spl0_1
| ~ spl0_83
| ~ spl0_177 ),
inference(forward_demodulation,[],[f1458,f546]) ).
fof(f1458,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_83
| ~ spl0_177 ),
inference(resolution,[],[f1361,f956]) ).
fof(f1361,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1360]) ).
fof(f1703,plain,
( spl0_227
| ~ spl0_1
| ~ spl0_85
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1449,f1344,f964,f544,f1701]) ).
fof(f1701,plain,
( spl0_227
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_k____,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f964,plain,
( spl0_85
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1344,plain,
( spl0_173
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1449,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,v_k____,tc_Complex_Ocomplex) = X0
| ~ spl0_1
| ~ spl0_85
| ~ spl0_173 ),
inference(forward_demodulation,[],[f1447,f546]) ).
fof(f1447,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_85
| ~ spl0_173 ),
inference(resolution,[],[f1345,f966]) ).
fof(f966,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f1345,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1344]) ).
fof(f1699,plain,
spl0_226,
inference(avatar_split_clause,[],[f403,f1697]) ).
fof(f1697,plain,
( spl0_226
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f403,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f1695,plain,
spl0_225,
inference(avatar_split_clause,[],[f385,f1693]) ).
fof(f1693,plain,
( spl0_225
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f385,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f1691,plain,
spl0_224,
inference(avatar_split_clause,[],[f380,f1689]) ).
fof(f1689,plain,
( spl0_224
<=> ! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f380,axiom,
! [X2,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f1687,plain,
spl0_223,
inference(avatar_split_clause,[],[f361,f1685]) ).
fof(f1685,plain,
( spl0_223
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f361,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f1683,plain,
spl0_222,
inference(avatar_split_clause,[],[f359,f1681]) ).
fof(f1681,plain,
( spl0_222
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f359,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f1679,plain,
spl0_221,
inference(avatar_split_clause,[],[f297,f1677]) ).
fof(f1677,plain,
( spl0_221
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f297,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f1675,plain,
spl0_220,
inference(avatar_split_clause,[],[f261,f1673]) ).
fof(f1673,plain,
( spl0_220
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X6,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f261,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X6,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1671,plain,
spl0_219,
inference(avatar_split_clause,[],[f259,f1669]) ).
fof(f1669,plain,
( spl0_219
<=> ! [X0,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f259,axiom,
! [X0,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f1667,plain,
spl0_218,
inference(avatar_split_clause,[],[f250,f1665]) ).
fof(f1665,plain,
( spl0_218
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f250,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f1663,plain,
spl0_217,
inference(avatar_split_clause,[],[f242,f1661]) ).
fof(f1661,plain,
( spl0_217
<=> ! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f242,axiom,
! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__zero_0) ).
fof(f1659,plain,
( spl0_216
| ~ spl0_1
| ~ spl0_77
| ~ spl0_172 ),
inference(avatar_split_clause,[],[f1445,f1340,f924,f544,f1657]) ).
fof(f1657,plain,
( spl0_216
<=> ! [X0] : v_k____ = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f924,plain,
( spl0_77
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1340,plain,
( spl0_172
<=> ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1445,plain,
( ! [X0] : v_k____ = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_77
| ~ spl0_172 ),
inference(forward_demodulation,[],[f1443,f546]) ).
fof(f1443,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_77
| ~ spl0_172 ),
inference(resolution,[],[f1341,f926]) ).
fof(f926,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f1341,plain,
( ! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) )
| ~ spl0_172 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1655,plain,
spl0_215,
inference(avatar_split_clause,[],[f216,f1653]) ).
fof(f1653,plain,
( spl0_215
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X6,X0),X6,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f216,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X6,X0),X6,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f1651,plain,
spl0_214,
inference(avatar_split_clause,[],[f186,f1649]) ).
fof(f1649,plain,
( spl0_214
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f186,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f1647,plain,
spl0_213,
inference(avatar_split_clause,[],[f185,f1645]) ).
fof(f1645,plain,
( spl0_213
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f185,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f1643,plain,
spl0_212,
inference(avatar_split_clause,[],[f184,f1641]) ).
fof(f1641,plain,
( spl0_212
<=> ! [X6,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f184,axiom,
! [X0,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
fof(f1639,plain,
spl0_211,
inference(avatar_split_clause,[],[f161,f1637]) ).
fof(f1637,plain,
( spl0_211
<=> ! [X2,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f161,axiom,
! [X2,X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X2,X3,X0) = c_HOL_Otimes__class_Otimes(X3,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1635,plain,
spl0_210,
inference(avatar_split_clause,[],[f160,f1633]) ).
fof(f1633,plain,
( spl0_210
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f160,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f1631,plain,
spl0_209,
inference(avatar_split_clause,[],[f159,f1629]) ).
fof(f1629,plain,
( spl0_209
<=> ! [X6,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X6,X0),X6,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f159,axiom,
! [X0,X1,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X6,X0),X6,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f1627,plain,
spl0_208,
inference(avatar_split_clause,[],[f141,f1625]) ).
fof(f1625,plain,
( spl0_208
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f141,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f1623,plain,
spl0_207,
inference(avatar_split_clause,[],[f118,f1621]) ).
fof(f1621,plain,
( spl0_207
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f118,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f1619,plain,
spl0_206,
inference(avatar_split_clause,[],[f100,f1617]) ).
fof(f1617,plain,
( spl0_206
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f100,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f1615,plain,
spl0_205,
inference(avatar_split_clause,[],[f93,f1613]) ).
fof(f1613,plain,
( spl0_205
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f93,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
fof(f1562,plain,
spl0_204,
inference(avatar_split_clause,[],[f399,f1560]) ).
fof(f1560,plain,
( spl0_204
<=> ! [X2,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f399,axiom,
! [X2,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f1558,plain,
( spl0_203
| ~ spl0_1
| ~ spl0_63
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1440,f1332,f854,f544,f1555]) ).
fof(f1555,plain,
( spl0_203
<=> v_k____ = c_HOL_Oinverse__class_Oinverse(v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f854,plain,
( spl0_63
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1332,plain,
( spl0_170
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1440,plain,
( v_k____ = c_HOL_Oinverse__class_Oinverse(v_k____,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_63
| ~ spl0_170 ),
inference(forward_demodulation,[],[f1439,f546]) ).
fof(f1439,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_63
| ~ spl0_170 ),
inference(resolution,[],[f1333,f856]) ).
fof(f856,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f1333,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1332]) ).
fof(f1553,plain,
spl0_202,
inference(avatar_split_clause,[],[f396,f1551]) ).
fof(f1551,plain,
( spl0_202
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f396,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f1549,plain,
spl0_201,
inference(avatar_split_clause,[],[f393,f1547]) ).
fof(f393,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f1545,plain,
spl0_200,
inference(avatar_split_clause,[],[f389,f1543]) ).
fof(f1543,plain,
( spl0_200
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f389,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f1541,plain,
spl0_199,
inference(avatar_split_clause,[],[f388,f1539]) ).
fof(f388,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f1537,plain,
spl0_198,
inference(avatar_split_clause,[],[f383,f1535]) ).
fof(f1535,plain,
( spl0_198
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f383,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f1533,plain,
spl0_197,
inference(avatar_split_clause,[],[f374,f1531]) ).
fof(f1531,plain,
( spl0_197
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f374,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f1529,plain,
spl0_196,
inference(avatar_split_clause,[],[f373,f1527]) ).
fof(f1527,plain,
( spl0_196
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f373,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f1525,plain,
spl0_195,
inference(avatar_split_clause,[],[f352,f1523]) ).
fof(f1523,plain,
( spl0_195
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f352,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
fof(f1521,plain,
spl0_194,
inference(avatar_split_clause,[],[f351,f1519]) ).
fof(f1519,plain,
( spl0_194
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f351,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f1517,plain,
spl0_193,
inference(avatar_split_clause,[],[f349,f1515]) ).
fof(f1515,plain,
( spl0_193
<=> ! [X6,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f349,axiom,
! [X0,X6] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f1513,plain,
spl0_192,
inference(avatar_split_clause,[],[f348,f1511]) ).
fof(f1511,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f348,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
fof(f1509,plain,
spl0_191,
inference(avatar_split_clause,[],[f345,f1507]) ).
fof(f1507,plain,
( spl0_191
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f345,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f1505,plain,
spl0_190,
inference(avatar_split_clause,[],[f344,f1503]) ).
fof(f1503,plain,
( spl0_190
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f344,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f1501,plain,
spl0_189,
inference(avatar_split_clause,[],[f343,f1499]) ).
fof(f343,axiom,
! [X0,X6] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1497,plain,
spl0_188,
inference(avatar_split_clause,[],[f342,f1495]) ).
fof(f342,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f1493,plain,
spl0_187,
inference(avatar_split_clause,[],[f289,f1491]) ).
fof(f1491,plain,
( spl0_187
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f289,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f1489,plain,
spl0_186,
inference(avatar_split_clause,[],[f235,f1487]) ).
fof(f1487,plain,
( spl0_186
<=> ! [X9,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f235,axiom,
! [X0,X9] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f1473,plain,
( spl0_185
| ~ spl0_1
| ~ spl0_67
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1427,f1316,f874,f544,f1470]) ).
fof(f1470,plain,
( spl0_185
<=> v_k____ = c_HOL_Osgn__class_Osgn(v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1316,plain,
( spl0_166
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1427,plain,
( v_k____ = c_HOL_Osgn__class_Osgn(v_k____,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_67
| ~ spl0_166 ),
inference(forward_demodulation,[],[f1426,f546]) ).
fof(f1426,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_67
| ~ spl0_166 ),
inference(resolution,[],[f1317,f876]) ).
fof(f1317,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1316]) ).
fof(f1437,plain,
( spl0_184
| ~ spl0_1
| ~ spl0_85
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1420,f1300,f964,f544,f1434]) ).
fof(f1434,plain,
( spl0_184
<=> v_k____ = c_HOL_Ouminus__class_Ouminus(v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1300,plain,
( spl0_162
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1420,plain,
( v_k____ = c_HOL_Ouminus__class_Ouminus(v_k____,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_85
| ~ spl0_162 ),
inference(forward_demodulation,[],[f1418,f546]) ).
fof(f1418,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_85
| ~ spl0_162 ),
inference(resolution,[],[f1301,f966]) ).
fof(f1301,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1300]) ).
fof(f1391,plain,
( ~ spl0_74
| ~ spl0_183
| ~ spl0_1
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1219,f1215,f544,f1388,f909]) ).
fof(f909,plain,
( spl0_74
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1388,plain,
( spl0_183
<=> v_k____ = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1215,plain,
( spl0_143
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1219,plain,
( v_k____ != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_143 ),
inference(superposition,[],[f1216,f546]) ).
fof(f1216,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1215]) ).
fof(f1382,plain,
spl0_182,
inference(avatar_split_clause,[],[f406,f1380]) ).
fof(f1380,plain,
( spl0_182
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f406,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1378,plain,
spl0_181,
inference(avatar_split_clause,[],[f405,f1376]) ).
fof(f1376,plain,
( spl0_181
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f405,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1374,plain,
spl0_180,
inference(avatar_split_clause,[],[f404,f1372]) ).
fof(f1372,plain,
( spl0_180
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f404,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f1370,plain,
spl0_179,
inference(avatar_split_clause,[],[f402,f1368]) ).
fof(f1368,plain,
( spl0_179
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f402,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1366,plain,
spl0_178,
inference(avatar_split_clause,[],[f401,f1364]) ).
fof(f401,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1362,plain,
spl0_177,
inference(avatar_split_clause,[],[f400,f1360]) ).
fof(f400,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1358,plain,
spl0_176,
inference(avatar_split_clause,[],[f386,f1356]) ).
fof(f1356,plain,
( spl0_176
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f386,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f1354,plain,
spl0_175,
inference(avatar_split_clause,[],[f382,f1352]) ).
fof(f1352,plain,
( spl0_175
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f382,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__0_0) ).
fof(f1350,plain,
spl0_174,
inference(avatar_split_clause,[],[f379,f1348]) ).
fof(f1348,plain,
( spl0_174
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f379,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1346,plain,
spl0_173,
inference(avatar_split_clause,[],[f378,f1344]) ).
fof(f378,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1342,plain,
spl0_172,
inference(avatar_split_clause,[],[f376,f1340]) ).
fof(f376,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1338,plain,
spl0_171,
inference(avatar_split_clause,[],[f365,f1336]) ).
fof(f1336,plain,
( spl0_171
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f365,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__0_0) ).
fof(f1334,plain,
spl0_170,
inference(avatar_split_clause,[],[f362,f1332]) ).
fof(f362,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f1330,plain,
spl0_169,
inference(avatar_split_clause,[],[f355,f1328]) ).
fof(f1328,plain,
( spl0_169
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f355,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1326,plain,
spl0_168,
inference(avatar_split_clause,[],[f354,f1324]) ).
fof(f1324,plain,
( spl0_168
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f354,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1322,plain,
spl0_167,
inference(avatar_split_clause,[],[f341,f1320]) ).
fof(f1320,plain,
( spl0_167
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(X5,X0)
| c_HOL_Ozero__class_Ozero(X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f341,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(X5,X0)
| c_HOL_Ozero__class_Ozero(X0) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__def_0) ).
fof(f1318,plain,
spl0_166,
inference(avatar_split_clause,[],[f340,f1316]) ).
fof(f340,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
fof(f1314,plain,
spl0_165,
inference(avatar_split_clause,[],[f339,f1312]) ).
fof(f1312,plain,
( spl0_165
<=> ! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f339,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).
fof(f1310,plain,
( ~ spl0_64
| spl0_164
| ~ spl0_1
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1218,f1211,f544,f1308,f859]) ).
fof(f859,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1308,plain,
( spl0_164
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1211,plain,
( spl0_142
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1218,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,v_k____,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
| ~ spl0_1
| ~ spl0_142 ),
inference(superposition,[],[f1212,f546]) ).
fof(f1212,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1211]) ).
fof(f1306,plain,
spl0_163,
inference(avatar_split_clause,[],[f338,f1304]) ).
fof(f1304,plain,
( spl0_163
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f338,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
fof(f1302,plain,
spl0_162,
inference(avatar_split_clause,[],[f333,f1300]) ).
fof(f333,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1298,plain,
spl0_161,
inference(avatar_split_clause,[],[f332,f1296]) ).
fof(f1296,plain,
( spl0_161
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f332,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1294,plain,
spl0_160,
inference(avatar_split_clause,[],[f298,f1292]) ).
fof(f1292,plain,
( spl0_160
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f298,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f1290,plain,
spl0_159,
inference(avatar_split_clause,[],[f224,f1288]) ).
fof(f1288,plain,
( spl0_159
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f224,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f1286,plain,
spl0_158,
inference(avatar_split_clause,[],[f219,f1284]) ).
fof(f1284,plain,
( spl0_158
<=> ! [X6,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f219,axiom,
! [X0,X6] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
fof(f1282,plain,
spl0_157,
inference(avatar_split_clause,[],[f193,f1280]) ).
fof(f1280,plain,
( spl0_157
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f193,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__one_0) ).
fof(f1278,plain,
spl0_156,
inference(avatar_split_clause,[],[f153,f1276]) ).
fof(f1276,plain,
( spl0_156
<=> ! [X6,X0,X19] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Otimes__class_Otimes(X6,X19,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f153,axiom,
! [X0,X6,X19] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Otimes__class_Otimes(X6,X19,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f1274,plain,
spl0_155,
inference(avatar_split_clause,[],[f152,f1272]) ).
fof(f1272,plain,
( spl0_155
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X6,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f152,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X6,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f1270,plain,
spl0_154,
inference(avatar_split_clause,[],[f151,f1268]) ).
fof(f1268,plain,
( spl0_154
<=> ! [X6,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f151,axiom,
! [X0,X1,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X6,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f1266,plain,
spl0_153,
inference(avatar_split_clause,[],[f150,f1264]) ).
fof(f1264,plain,
( spl0_153
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f150,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f1262,plain,
spl0_152,
inference(avatar_split_clause,[],[f149,f1260]) ).
fof(f1260,plain,
( spl0_152
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f149,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f1258,plain,
spl0_151,
inference(avatar_split_clause,[],[f147,f1256]) ).
fof(f1256,plain,
( spl0_151
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f147,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f1254,plain,
spl0_150,
inference(avatar_split_clause,[],[f146,f1252]) ).
fof(f1252,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f146,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f1250,plain,
spl0_149,
inference(avatar_split_clause,[],[f145,f1248]) ).
fof(f1248,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f145,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f1246,plain,
spl0_148,
inference(avatar_split_clause,[],[f117,f1244]) ).
fof(f1244,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f1242,plain,
spl0_147,
inference(avatar_split_clause,[],[f79,f1240]) ).
fof(f1240,plain,
( spl0_147
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f79,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f1233,plain,
spl0_146,
inference(avatar_split_clause,[],[f408,f1230]) ).
fof(f408,axiom,
v_s____ = c_Polynomial_OpCons(v_k____,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1228,plain,
( ~ spl0_76
| spl0_145
| ~ spl0_1
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1205,f1202,f544,f1225,f919]) ).
fof(f919,plain,
( spl0_76
<=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1225,plain,
( spl0_145
<=> c_Int_Oiszero(v_k____,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1202,plain,
( spl0_140
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1205,plain,
( c_Int_Oiszero(v_k____,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_140 ),
inference(superposition,[],[f1203,f546]) ).
fof(f1203,plain,
( ! [X0] :
( c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Osemiring__1(X0) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1223,plain,
spl0_144,
inference(avatar_split_clause,[],[f300,f1221]) ).
fof(f1221,plain,
( spl0_144
<=> ! [X2,X3] :
( X2 = X3
| c_Complex_Ocnj(X2) != c_Complex_Ocnj(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f300,axiom,
! [X2,X3] :
( X2 = X3
| c_Complex_Ocnj(X2) != c_Complex_Ocnj(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
fof(f1217,plain,
spl0_143,
inference(avatar_split_clause,[],[f369,f1215]) ).
fof(f369,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1213,plain,
spl0_142,
inference(avatar_split_clause,[],[f353,f1211]) ).
fof(f353,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1209,plain,
spl0_141,
inference(avatar_split_clause,[],[f1,f1207]) ).
fof(f1207,plain,
( spl0_141
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1204,plain,
spl0_140,
inference(avatar_split_clause,[],[f331,f1202]) ).
fof(f331,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iszero__0_0) ).
fof(f1200,plain,
spl0_139,
inference(avatar_split_clause,[],[f315,f1198]) ).
fof(f1198,plain,
( spl0_139
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f315,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
fof(f1196,plain,
spl0_138,
inference(avatar_split_clause,[],[f12,f1194]) ).
fof(f1194,plain,
( spl0_138
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f12,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1191,plain,
( spl0_137
| ~ spl0_3
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f1187,f1025,f554,f1189]) ).
fof(f1189,plain,
( spl0_137
<=> ! [X0] :
( v_k____ != X0
| v_k____ = c_Complex_Ocnj(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f554,plain,
( spl0_3
<=> ! [X5] :
( c_Complex_Ocnj(X5) != v_k____
| v_k____ = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1025,plain,
( spl0_97
<=> ! [X5] : c_Complex_Ocnj(c_Complex_Ocnj(X5)) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1187,plain,
( ! [X0] :
( v_k____ != X0
| v_k____ = c_Complex_Ocnj(X0) )
| ~ spl0_3
| ~ spl0_97 ),
inference(superposition,[],[f555,f1026]) ).
fof(f1026,plain,
( ! [X5] : c_Complex_Ocnj(c_Complex_Ocnj(X5)) = X5
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f555,plain,
( ! [X5] :
( c_Complex_Ocnj(X5) != v_k____
| v_k____ = X5 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f1185,plain,
spl0_136,
inference(avatar_split_clause,[],[f539,f1183]) ).
fof(f1183,plain,
( spl0_136
<=> ! [X32] :
( ~ class_HOL_Ozero(X32)
| class_HOL_Ozero(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f539,axiom,
! [X32] :
( ~ class_HOL_Ozero(X32)
| class_HOL_Ozero(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1181,plain,
spl0_135,
inference(avatar_split_clause,[],[f538,f1179]) ).
fof(f1179,plain,
( spl0_135
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Power_Opower(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f538,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Power_Opower(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(f1177,plain,
spl0_134,
inference(avatar_split_clause,[],[f537,f1175]) ).
fof(f1175,plain,
( spl0_134
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f537,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1173,plain,
spl0_133,
inference(avatar_split_clause,[],[f536,f1171]) ).
fof(f1171,plain,
( spl0_133
<=> ! [X32] :
( ~ class_Ring__and__Field_Ofield(X32)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f536,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ofield(X32)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f1169,plain,
spl0_132,
inference(avatar_split_clause,[],[f535,f1167]) ).
fof(f1167,plain,
( spl0_132
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f535,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(f1165,plain,
spl0_131,
inference(avatar_split_clause,[],[f534,f1163]) ).
fof(f1163,plain,
( spl0_131
<=> ! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f534,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1161,plain,
spl0_130,
inference(avatar_split_clause,[],[f533,f1159]) ).
fof(f1159,plain,
( spl0_130
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring(X32)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f533,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring(X32)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1157,plain,
spl0_129,
inference(avatar_split_clause,[],[f532,f1155]) ).
fof(f1155,plain,
( spl0_129
<=> ! [X32] :
( ~ class_Ring__and__Field_Ofield(X32)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f532,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ofield(X32)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1153,plain,
spl0_128,
inference(avatar_split_clause,[],[f531,f1151]) ).
fof(f1151,plain,
( spl0_128
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f531,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(f1149,plain,
spl0_127,
inference(avatar_split_clause,[],[f530,f1147]) ).
fof(f1147,plain,
( spl0_127
<=> ! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f530,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).
fof(f1145,plain,
spl0_126,
inference(avatar_split_clause,[],[f529,f1143]) ).
fof(f1143,plain,
( spl0_126
<=> ! [X32] :
( ~ class_OrderedGroup_Oab__group__add(X32)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f529,axiom,
! [X32] :
( ~ class_OrderedGroup_Oab__group__add(X32)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1141,plain,
spl0_125,
inference(avatar_split_clause,[],[f528,f1139]) ).
fof(f1139,plain,
( spl0_125
<=> ! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f528,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1137,plain,
spl0_124,
inference(avatar_split_clause,[],[f527,f1135]) ).
fof(f1135,plain,
( spl0_124
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f527,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1133,plain,
spl0_123,
inference(avatar_split_clause,[],[f526,f1131]) ).
fof(f1131,plain,
( spl0_123
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f526,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1129,plain,
spl0_122,
inference(avatar_split_clause,[],[f525,f1127]) ).
fof(f1127,plain,
( spl0_122
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring(X32)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f525,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring(X32)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1125,plain,
spl0_121,
inference(avatar_split_clause,[],[f524,f1123]) ).
fof(f1123,plain,
( spl0_121
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f524,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1121,plain,
spl0_120,
inference(avatar_split_clause,[],[f523,f1119]) ).
fof(f1119,plain,
( spl0_120
<=> ! [X32] :
( ~ class_OrderedGroup_Oab__group__add(X32)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f523,axiom,
! [X32] :
( ~ class_OrderedGroup_Oab__group__add(X32)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1117,plain,
spl0_119,
inference(avatar_split_clause,[],[f522,f1115]) ).
fof(f1115,plain,
( spl0_119
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f522,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) ).
fof(f1113,plain,
spl0_118,
inference(avatar_split_clause,[],[f521,f1111]) ).
fof(f1111,plain,
( spl0_118
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f521,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X32)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1109,plain,
spl0_117,
inference(avatar_split_clause,[],[f520,f1107]) ).
fof(f1107,plain,
( spl0_117
<=> ! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f520,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1105,plain,
spl0_116,
inference(avatar_split_clause,[],[f519,f1103]) ).
fof(f1103,plain,
( spl0_116
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f519,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1101,plain,
spl0_115,
inference(avatar_split_clause,[],[f518,f1099]) ).
fof(f1099,plain,
( spl0_115
<=> ! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f518,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1097,plain,
spl0_114,
inference(avatar_split_clause,[],[f517,f1095]) ).
fof(f1095,plain,
( spl0_114
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f517,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1093,plain,
spl0_113,
inference(avatar_split_clause,[],[f516,f1091]) ).
fof(f1091,plain,
( spl0_113
<=> ! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f516,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X32)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1089,plain,
spl0_112,
inference(avatar_split_clause,[],[f515,f1087]) ).
fof(f1087,plain,
( spl0_112
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f515,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1085,plain,
spl0_111,
inference(avatar_split_clause,[],[f514,f1083]) ).
fof(f1083,plain,
( spl0_111
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f514,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1081,plain,
spl0_110,
inference(avatar_split_clause,[],[f513,f1079]) ).
fof(f1079,plain,
( spl0_110
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f513,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X32)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1077,plain,
spl0_109,
inference(avatar_split_clause,[],[f512,f1075]) ).
fof(f1075,plain,
( spl0_109
<=> ! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f512,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1073,plain,
spl0_108,
inference(avatar_split_clause,[],[f511,f1071]) ).
fof(f1071,plain,
( spl0_108
<=> ! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f511,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1069,plain,
spl0_107,
inference(avatar_split_clause,[],[f510,f1067]) ).
fof(f1067,plain,
( spl0_107
<=> ! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f510,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1065,plain,
spl0_106,
inference(avatar_split_clause,[],[f509,f1063]) ).
fof(f1063,plain,
( spl0_106
<=> ! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f509,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1061,plain,
spl0_105,
inference(avatar_split_clause,[],[f508,f1059]) ).
fof(f1059,plain,
( spl0_105
<=> ! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f508,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1057,plain,
( ~ spl0_104
| ~ spl0_1
| spl0_96 ),
inference(avatar_split_clause,[],[f1023,f1019,f544,f1054]) ).
fof(f1054,plain,
( spl0_104
<=> c_Complex_Oii = v_k____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1019,plain,
( spl0_96
<=> c_Complex_Oii = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1023,plain,
( c_Complex_Oii != v_k____
| ~ spl0_1
| spl0_96 ),
inference(superposition,[],[f1021,f546]) ).
fof(f1021,plain,
( c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| spl0_96 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1052,plain,
spl0_103,
inference(avatar_split_clause,[],[f507,f1050]) ).
fof(f1050,plain,
( spl0_103
<=> ! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f507,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1048,plain,
spl0_102,
inference(avatar_split_clause,[],[f506,f1046]) ).
fof(f1046,plain,
( spl0_102
<=> ! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f506,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oordered__idom(X32)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1044,plain,
spl0_101,
inference(avatar_split_clause,[],[f505,f1042]) ).
fof(f1042,plain,
( spl0_101
<=> ! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f505,axiom,
! [X32] :
( ~ class_Ring__and__Field_Oidom(X32)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1040,plain,
spl0_100,
inference(avatar_split_clause,[],[f412,f1038]) ).
fof(f1038,plain,
( spl0_100
<=> ! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f412,axiom,
! [X32] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X32)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1036,plain,
spl0_99,
inference(avatar_split_clause,[],[f411,f1034]) ).
fof(f1034,plain,
( spl0_99
<=> ! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X32)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f411,axiom,
! [X32] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X32)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X32)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1032,plain,
~ spl0_98,
inference(avatar_split_clause,[],[f299,f1029]) ).
fof(f299,axiom,
v_s____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sne_0) ).
fof(f1027,plain,
spl0_97,
inference(avatar_split_clause,[],[f255,f1025]) ).
fof(f255,axiom,
! [X5] : c_Complex_Ocnj(c_Complex_Ocnj(X5)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
fof(f1022,plain,
~ spl0_96,
inference(avatar_split_clause,[],[f330,f1019]) ).
fof(f330,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
fof(f1017,plain,
spl0_95,
inference(avatar_split_clause,[],[f504,f1014]) ).
fof(f504,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1012,plain,
spl0_94,
inference(avatar_split_clause,[],[f503,f1009]) ).
fof(f1009,plain,
( spl0_94
<=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f503,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
fof(f1007,plain,
spl0_93,
inference(avatar_split_clause,[],[f502,f1004]) ).
fof(f1004,plain,
( spl0_93
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f502,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1002,plain,
spl0_92,
inference(avatar_split_clause,[],[f501,f999]) ).
fof(f999,plain,
( spl0_92
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f501,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f997,plain,
spl0_91,
inference(avatar_split_clause,[],[f500,f994]) ).
fof(f994,plain,
( spl0_91
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f500,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(f992,plain,
spl0_90,
inference(avatar_split_clause,[],[f499,f989]) ).
fof(f989,plain,
( spl0_90
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f499,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f987,plain,
spl0_89,
inference(avatar_split_clause,[],[f498,f984]) ).
fof(f984,plain,
( spl0_89
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f498,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f982,plain,
spl0_88,
inference(avatar_split_clause,[],[f497,f979]) ).
fof(f497,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f977,plain,
spl0_87,
inference(avatar_split_clause,[],[f496,f974]) ).
fof(f974,plain,
( spl0_87
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f496,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f972,plain,
spl0_86,
inference(avatar_split_clause,[],[f495,f969]) ).
fof(f969,plain,
( spl0_86
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f495,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f967,plain,
spl0_85,
inference(avatar_split_clause,[],[f494,f964]) ).
fof(f494,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f962,plain,
spl0_84,
inference(avatar_split_clause,[],[f493,f959]) ).
fof(f959,plain,
( spl0_84
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f493,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
fof(f957,plain,
spl0_83,
inference(avatar_split_clause,[],[f492,f954]) ).
fof(f492,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f952,plain,
spl0_82,
inference(avatar_split_clause,[],[f491,f949]) ).
fof(f949,plain,
( spl0_82
<=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f491,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
fof(f947,plain,
spl0_81,
inference(avatar_split_clause,[],[f490,f944]) ).
fof(f944,plain,
( spl0_81
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f490,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f942,plain,
spl0_80,
inference(avatar_split_clause,[],[f489,f939]) ).
fof(f939,plain,
( spl0_80
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f489,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f937,plain,
spl0_79,
inference(avatar_split_clause,[],[f488,f934]) ).
fof(f934,plain,
( spl0_79
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f488,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f932,plain,
spl0_78,
inference(avatar_split_clause,[],[f487,f929]) ).
fof(f929,plain,
( spl0_78
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f487,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(f927,plain,
spl0_77,
inference(avatar_split_clause,[],[f486,f924]) ).
fof(f486,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f922,plain,
spl0_76,
inference(avatar_split_clause,[],[f485,f919]) ).
fof(f485,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
fof(f917,plain,
spl0_75,
inference(avatar_split_clause,[],[f484,f914]) ).
fof(f914,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f484,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f912,plain,
spl0_74,
inference(avatar_split_clause,[],[f483,f909]) ).
fof(f483,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f907,plain,
spl0_73,
inference(avatar_split_clause,[],[f482,f904]) ).
fof(f904,plain,
( spl0_73
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f482,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f902,plain,
spl0_72,
inference(avatar_split_clause,[],[f481,f899]) ).
fof(f899,plain,
( spl0_72
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f481,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f897,plain,
spl0_71,
inference(avatar_split_clause,[],[f480,f894]) ).
fof(f894,plain,
( spl0_71
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f480,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f892,plain,
spl0_70,
inference(avatar_split_clause,[],[f479,f889]) ).
fof(f889,plain,
( spl0_70
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f479,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f887,plain,
spl0_69,
inference(avatar_split_clause,[],[f478,f884]) ).
fof(f884,plain,
( spl0_69
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f478,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f882,plain,
spl0_68,
inference(avatar_split_clause,[],[f477,f879]) ).
fof(f879,plain,
( spl0_68
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f477,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f877,plain,
spl0_67,
inference(avatar_split_clause,[],[f476,f874]) ).
fof(f476,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f872,plain,
spl0_66,
inference(avatar_split_clause,[],[f475,f869]) ).
fof(f869,plain,
( spl0_66
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f475,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f867,plain,
spl0_65,
inference(avatar_split_clause,[],[f474,f864]) ).
fof(f864,plain,
( spl0_65
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f474,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f862,plain,
spl0_64,
inference(avatar_split_clause,[],[f473,f859]) ).
fof(f473,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(f857,plain,
spl0_63,
inference(avatar_split_clause,[],[f472,f854]) ).
fof(f472,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f852,plain,
spl0_62,
inference(avatar_split_clause,[],[f471,f849]) ).
fof(f849,plain,
( spl0_62
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f471,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(f847,plain,
spl0_61,
inference(avatar_split_clause,[],[f470,f844]) ).
fof(f844,plain,
( spl0_61
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f470,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(f842,plain,
spl0_60,
inference(avatar_split_clause,[],[f469,f839]) ).
fof(f839,plain,
( spl0_60
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f469,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f837,plain,
spl0_59,
inference(avatar_split_clause,[],[f468,f834]) ).
fof(f834,plain,
( spl0_59
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f468,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f832,plain,
spl0_58,
inference(avatar_split_clause,[],[f467,f829]) ).
fof(f829,plain,
( spl0_58
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f467,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f827,plain,
spl0_57,
inference(avatar_split_clause,[],[f466,f824]) ).
fof(f466,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(f822,plain,
spl0_56,
inference(avatar_split_clause,[],[f465,f819]) ).
fof(f819,plain,
( spl0_56
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f465,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f817,plain,
spl0_55,
inference(avatar_split_clause,[],[f464,f814]) ).
fof(f814,plain,
( spl0_55
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f464,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
fof(f812,plain,
spl0_54,
inference(avatar_split_clause,[],[f463,f809]) ).
fof(f809,plain,
( spl0_54
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f463,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f807,plain,
spl0_53,
inference(avatar_split_clause,[],[f462,f804]) ).
fof(f804,plain,
( spl0_53
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f462,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f802,plain,
spl0_52,
inference(avatar_split_clause,[],[f461,f799]) ).
fof(f799,plain,
( spl0_52
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f461,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f797,plain,
spl0_51,
inference(avatar_split_clause,[],[f460,f794]) ).
fof(f794,plain,
( spl0_51
<=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f460,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
fof(f792,plain,
spl0_50,
inference(avatar_split_clause,[],[f459,f789]) ).
fof(f789,plain,
( spl0_50
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f459,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f787,plain,
spl0_49,
inference(avatar_split_clause,[],[f458,f784]) ).
fof(f784,plain,
( spl0_49
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f458,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f782,plain,
spl0_48,
inference(avatar_split_clause,[],[f457,f779]) ).
fof(f779,plain,
( spl0_48
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f457,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f777,plain,
spl0_47,
inference(avatar_split_clause,[],[f456,f774]) ).
fof(f774,plain,
( spl0_47
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f456,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f772,plain,
spl0_46,
inference(avatar_split_clause,[],[f455,f769]) ).
fof(f769,plain,
( spl0_46
<=> class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f455,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
fof(f767,plain,
spl0_45,
inference(avatar_split_clause,[],[f454,f764]) ).
fof(f764,plain,
( spl0_45
<=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f454,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
fof(f762,plain,
spl0_44,
inference(avatar_split_clause,[],[f453,f759]) ).
fof(f759,plain,
( spl0_44
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f453,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f757,plain,
spl0_43,
inference(avatar_split_clause,[],[f452,f754]) ).
fof(f754,plain,
( spl0_43
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f452,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f752,plain,
spl0_42,
inference(avatar_split_clause,[],[f451,f749]) ).
fof(f749,plain,
( spl0_42
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f451,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f747,plain,
spl0_41,
inference(avatar_split_clause,[],[f450,f744]) ).
fof(f744,plain,
( spl0_41
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f450,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f742,plain,
spl0_40,
inference(avatar_split_clause,[],[f449,f739]) ).
fof(f739,plain,
( spl0_40
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f449,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f737,plain,
spl0_39,
inference(avatar_split_clause,[],[f448,f734]) ).
fof(f734,plain,
( spl0_39
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f448,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f732,plain,
spl0_38,
inference(avatar_split_clause,[],[f447,f729]) ).
fof(f729,plain,
( spl0_38
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f447,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f727,plain,
spl0_37,
inference(avatar_split_clause,[],[f446,f724]) ).
fof(f724,plain,
( spl0_37
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f446,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(f722,plain,
spl0_36,
inference(avatar_split_clause,[],[f445,f719]) ).
fof(f719,plain,
( spl0_36
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f445,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f717,plain,
spl0_35,
inference(avatar_split_clause,[],[f444,f714]) ).
fof(f714,plain,
( spl0_35
<=> class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f444,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) ).
fof(f712,plain,
spl0_34,
inference(avatar_split_clause,[],[f443,f709]) ).
fof(f709,plain,
( spl0_34
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f443,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f707,plain,
spl0_33,
inference(avatar_split_clause,[],[f442,f704]) ).
fof(f704,plain,
( spl0_33
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f442,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(f702,plain,
spl0_32,
inference(avatar_split_clause,[],[f441,f699]) ).
fof(f699,plain,
( spl0_32
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f441,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f697,plain,
spl0_31,
inference(avatar_split_clause,[],[f440,f694]) ).
fof(f694,plain,
( spl0_31
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f440,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f692,plain,
spl0_30,
inference(avatar_split_clause,[],[f439,f689]) ).
fof(f689,plain,
( spl0_30
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f439,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f687,plain,
spl0_29,
inference(avatar_split_clause,[],[f438,f684]) ).
fof(f684,plain,
( spl0_29
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f438,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f682,plain,
spl0_28,
inference(avatar_split_clause,[],[f437,f679]) ).
fof(f679,plain,
( spl0_28
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f437,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f677,plain,
spl0_27,
inference(avatar_split_clause,[],[f436,f674]) ).
fof(f674,plain,
( spl0_27
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f436,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f672,plain,
spl0_26,
inference(avatar_split_clause,[],[f435,f669]) ).
fof(f669,plain,
( spl0_26
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f435,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f667,plain,
spl0_25,
inference(avatar_split_clause,[],[f434,f664]) ).
fof(f664,plain,
( spl0_25
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f434,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f662,plain,
spl0_24,
inference(avatar_split_clause,[],[f433,f659]) ).
fof(f659,plain,
( spl0_24
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f433,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f657,plain,
spl0_23,
inference(avatar_split_clause,[],[f432,f654]) ).
fof(f654,plain,
( spl0_23
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f432,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f652,plain,
spl0_22,
inference(avatar_split_clause,[],[f431,f649]) ).
fof(f649,plain,
( spl0_22
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f431,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f647,plain,
spl0_21,
inference(avatar_split_clause,[],[f430,f644]) ).
fof(f644,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f430,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(f642,plain,
spl0_20,
inference(avatar_split_clause,[],[f429,f639]) ).
fof(f639,plain,
( spl0_20
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f429,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f637,plain,
spl0_19,
inference(avatar_split_clause,[],[f428,f634]) ).
fof(f634,plain,
( spl0_19
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f428,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(f632,plain,
spl0_18,
inference(avatar_split_clause,[],[f427,f629]) ).
fof(f629,plain,
( spl0_18
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f427,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(f627,plain,
spl0_17,
inference(avatar_split_clause,[],[f426,f624]) ).
fof(f624,plain,
( spl0_17
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f426,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f622,plain,
spl0_16,
inference(avatar_split_clause,[],[f425,f619]) ).
fof(f619,plain,
( spl0_16
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f425,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(f617,plain,
spl0_15,
inference(avatar_split_clause,[],[f424,f614]) ).
fof(f614,plain,
( spl0_15
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f424,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(f612,plain,
spl0_14,
inference(avatar_split_clause,[],[f423,f609]) ).
fof(f609,plain,
( spl0_14
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f423,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f607,plain,
spl0_13,
inference(avatar_split_clause,[],[f422,f604]) ).
fof(f604,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f422,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(f602,plain,
spl0_12,
inference(avatar_split_clause,[],[f421,f599]) ).
fof(f599,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f421,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f597,plain,
spl0_11,
inference(avatar_split_clause,[],[f420,f594]) ).
fof(f594,plain,
( spl0_11
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f420,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(f592,plain,
spl0_10,
inference(avatar_split_clause,[],[f419,f589]) ).
fof(f589,plain,
( spl0_10
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f419,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(f587,plain,
spl0_9,
inference(avatar_split_clause,[],[f418,f584]) ).
fof(f584,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f418,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(f582,plain,
spl0_8,
inference(avatar_split_clause,[],[f417,f579]) ).
fof(f579,plain,
( spl0_8
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f417,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f577,plain,
spl0_7,
inference(avatar_split_clause,[],[f416,f574]) ).
fof(f574,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f416,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f572,plain,
spl0_6,
inference(avatar_split_clause,[],[f415,f569]) ).
fof(f569,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f415,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f567,plain,
spl0_5,
inference(avatar_split_clause,[],[f414,f564]) ).
fof(f564,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f414,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f562,plain,
spl0_4,
inference(avatar_split_clause,[],[f413,f559]) ).
fof(f559,plain,
( spl0_4
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f413,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f556,plain,
spl0_3,
inference(avatar_split_clause,[],[f542,f554]) ).
fof(f542,plain,
! [X5] :
( c_Complex_Ocnj(X5) != v_k____
| v_k____ = X5 ),
inference(forward_demodulation,[],[f541,f410]) ).
fof(f410,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = v_k____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f541,plain,
! [X5] :
( v_k____ = X5
| c_Complex_Ocnj(X5) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[],[f334,f410]) ).
fof(f334,axiom,
! [X5] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X5
| c_Complex_Ocnj(X5) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
fof(f552,plain,
spl0_2,
inference(avatar_split_clause,[],[f540,f549]) ).
fof(f549,plain,
( spl0_2
<=> v_k____ = c_Complex_Ocnj(v_k____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f540,plain,
v_k____ = c_Complex_Ocnj(v_k____),
inference(forward_demodulation,[],[f384,f410]) ).
fof(f384,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
fof(f547,plain,
spl0_1,
inference(avatar_split_clause,[],[f410,f544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG417-1 : TPTP v8.2.0. Released v4.1.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n021.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 22:58:23 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.37 % (24729)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.41 % (24730)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.41 % (24734)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)
% 0.23/0.41 % (24733)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.41 % (24731)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.41 % (24735)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)
% 0.23/0.41 % (24736)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)
% 0.23/0.42 % (24732)WARNING: value z3 for option sas not known
% 0.23/0.42 % (24732)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)
% 0.23/0.45 TRYING [1]
% 0.23/0.45 % (24734)First to succeed.
% 0.23/0.46 TRYING [2]
% 0.23/0.46 % (24734)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24729"
% 0.23/0.46 % (24734)Refutation found. Thanks to Tanya!
% 0.23/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.47 % (24734)------------------------------
% 0.23/0.47 % (24734)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.23/0.47 % (24734)Termination reason: Refutation
% 0.23/0.47
% 0.23/0.47 % (24734)Memory used [KB]: 1990
% 0.23/0.47 % (24734)Time elapsed: 0.055 s
% 0.23/0.47 % (24734)Instructions burned: 87 (million)
% 0.23/0.47 % (24729)Success in time 0.085 s
%------------------------------------------------------------------------------