%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG434-1 : 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 : n011.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 18:37:51 EDT 2024

% Result   : Unsatisfiable 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  473
% Syntax   : Number of formulae    :  758 ( 264 unt;   0 def)
%            Number of atoms       : 1618 ( 347 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives : 1474 ( 614   ~; 616   |;   0   &)
%                                         ( 244 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :  285 ( 283 usr; 245 prp; 0-5 aty)
%            Number of functors    :   19 (  19 usr;   4 con; 0-3 aty)
%            Number of variables   :  981 ( 981   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1973,plain,
    $false,
    inference(avatar_sat_refutation,[],[f446,f451,f456,f461,f466,f471,f476,f481,f486,f491,f496,f501,f506,f511,f516,f521,f526,f531,f536,f541,f546,f551,f556,f561,f566,f571,f576,f581,f586,f591,f596,f601,f606,f610,f614,f618,f622,f626,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f678,f682,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f746,f750,f754,f758,f762,f767,f771,f775,f779,f783,f787,f791,f795,f799,f803,f807,f811,f815,f819,f823,f827,f831,f835,f839,f843,f847,f851,f855,f859,f863,f867,f871,f884,f907,f923,f927,f931,f935,f939,f943,f947,f951,f955,f959,f963,f967,f971,f975,f979,f983,f992,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1107,f1121,f1145,f1168,f1172,f1176,f1180,f1184,f1188,f1192,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1258,f1318,f1322,f1326,f1333,f1337,f1341,f1345,f1349,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1401,f1405,f1409,f1493,f1520,f1524,f1528,f1532,f1536,f1540,f1544,f1558,f1562,f1566,f1570,f1574,f1578,f1582,f1586,f1590,f1594,f1607,f1611,f1615,f1619,f1623,f1667,f1722,f1726,f1730,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1852,f1971,f1972]) ).

fof(f1972,plain,
    ( ~ spl0_8
    | ~ spl0_33
    | spl0_1
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f1965,f1832,f443,f603,f478]) ).

fof(f478,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f603,plain,
    ( spl0_33
  <=> c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f443,plain,
    ( spl0_1
  <=> c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f1832,plain,
    ( spl0_242
  <=> ! [X3,X0,X5,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X5,X3,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f1965,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | spl0_1
    | ~ spl0_242 ),
    inference(resolution,[],[f1833,f445]) ).

fof(f445,plain,
    ( ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f443]) ).

fof(f1833,plain,
    ( ! [X3,X0,X1,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X5,X3,X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f1832]) ).

fof(f1971,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f8,f1969]) ).

fof(f1969,plain,
    ( spl0_244
  <=> ! [X6,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f8,axiom,
    ! [X0,X1,X6] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X1,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).

fof(f1852,plain,
    ( spl0_243
    | ~ spl0_8
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f995,f945,f478,f1850]) ).

fof(f1850,plain,
    ( spl0_243
  <=> ! [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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f945,plain,
    ( spl0_108
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f995,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_8
    | ~ spl0_108 ),
    inference(resolution,[],[f946,f480]) ).

fof(f480,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f946,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f945]) ).

fof(f1834,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f367,f1832]) ).

fof(f367,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X5,X3,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).

fof(f1830,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f366,f1828]) ).

fof(f1828,plain,
    ( spl0_241
  <=> ! [X5,X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f366,axiom,
    ! [X3,X0,X1,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X3,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).

fof(f1826,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f326,f1824]) ).

fof(f1824,plain,
    ( spl0_240
  <=> ! [X0,X12,X6,X21] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X21,X6,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_Polynomial_Opoly__gcd(X6,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f326,axiom,
    ! [X21,X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X21,X6,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_Polynomial_Opoly__gcd(X6,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).

fof(f1822,plain,
    ( spl0_239
    | ~ spl0_8
    | ~ spl0_107 ),
    inference(avatar_split_clause,[],[f993,f941,f478,f1820]) ).

fof(f1820,plain,
    ( spl0_239
  <=> ! [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) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f941,plain,
    ( spl0_107
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f993,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_8
    | ~ spl0_107 ),
    inference(resolution,[],[f942,f480]) ).

fof(f942,plain,
    ( ! [X0,X5] :
        ( ~ 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),X5,X0) )
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f941]) ).

fof(f1818,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f325,f1816]) ).

fof(f1816,plain,
    ( spl0_238
  <=> ! [X0,X12,X6,X21] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X21,X12,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_Polynomial_Opoly__gcd(X6,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f325,axiom,
    ! [X21,X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X21,X12,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X21,c_Polynomial_Opoly__gcd(X6,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).

fof(f1814,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f288,f1812]) ).

fof(f1812,plain,
    ( spl0_237
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f288,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

fof(f1810,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f263,f1808]) ).

fof(f1808,plain,
    ( spl0_236
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Otimes__class_Otimes(X5,X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f263,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Otimes__class_Otimes(X5,X5,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X5,X0),c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).

fof(f1806,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f255,f1804]) ).

fof(f1804,plain,
    ( spl0_235
  <=> ! [X6,X4,X0,X12,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Polynomial_Opdivmod__rel(X6,X12,X3,X4,X0)
        | c_Divides_Odiv__class_Odiv(X6,X12,tc_Polynomial_Opoly(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f255,axiom,
    ! [X3,X0,X6,X4,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Polynomial_Opdivmod__rel(X6,X12,X3,X4,X0)
      | c_Divides_Odiv__class_Odiv(X6,X12,tc_Polynomial_Opoly(X0)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).

fof(f1802,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f185,f1800]) ).

fof(f1800,plain,
    ( spl0_234
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X5,X0) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f185,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X7,X5,X0),X5,X0) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).

fof(f1798,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f184,f1796]) ).

fof(f1796,plain,
    ( spl0_233
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X7,X5,X0),X0) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f184,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | c_HOL_Otimes__class_Otimes(X5,c_Divides_Odiv__class_Odiv(X7,X5,X0),X0) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).

fof(f1794,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f179,f1792]) ).

fof(f1792,plain,
    ( spl0_232
  <=> ! [X5,X0,X17] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X17,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X5,X0),X17,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f179,axiom,
    ! [X0,X17,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X5,X17,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X5,X0),X17,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).

fof(f1790,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f163,f1788]) ).

fof(f1788,plain,
    ( spl0_231
  <=> ! [X6,X4,X0,X12,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Polynomial_Opdivmod__rel(X6,X12,X3,X4,X0)
        | c_Divides_Odiv__class_Omod(X6,X12,tc_Polynomial_Opoly(X0)) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f163,axiom,
    ! [X3,X0,X6,X4,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Polynomial_Opdivmod__rel(X6,X12,X3,X4,X0)
      | c_Divides_Odiv__class_Omod(X6,X12,tc_Polynomial_Opoly(X0)) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__poly__eq_0) ).

fof(f1786,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f101,f1784]) ).

fof(f1784,plain,
    ( spl0_230
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f101,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Otimes__class_Otimes(X5,X7,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

fof(f1782,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f100,f1780]) ).

fof(f1780,plain,
    ( spl0_229
  <=> ! [X0,X7] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(X7,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f100,axiom,
    ! [X0,X7] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X7,X0),c_HOL_Ouminus__class_Ouminus(X7,X0),X0) = c_HOL_Otimes__class_Otimes(X7,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

fof(f1778,plain,
    ( spl0_228
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(avatar_split_clause,[],[f987,f937,f543,f1776]) ).

fof(f1776,plain,
    ( spl0_228
  <=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f543,plain,
    ( spl0_21
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f937,plain,
    ( spl0_106
  <=> ! [X0,X17] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X17,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f987,plain,
    ( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
    | ~ spl0_21
    | ~ spl0_106 ),
    inference(resolution,[],[f938,f545]) ).

fof(f545,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f543]) ).

fof(f938,plain,
    ( ! [X0,X17] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X17,X0) )
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f937]) ).

fof(f1774,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f98,f1772]) ).

fof(f1772,plain,
    ( spl0_227
  <=> ! [X5,X0,X7] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f98,axiom,
    ! [X0,X7,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).

fof(f1770,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f96,f1768]) ).

fof(f1768,plain,
    ( spl0_226
  <=> ! [X5,X0,X7] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f96,axiom,
    ! [X0,X7,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

fof(f1766,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f90,f1764]) ).

fof(f1764,plain,
    ( spl0_225
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X6,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f90,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X6,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).

fof(f1762,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f89,f1760]) ).

fof(f1760,plain,
    ( spl0_224
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X6,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f89,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X6
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X6,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).

fof(f1758,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f88,f1756]) ).

fof(f1756,plain,
    ( spl0_223
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f88,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X7,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).

fof(f1754,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f61,f1752]) ).

fof(f1752,plain,
    ( spl0_222
  <=> ! [X6,X4,X0,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3
        | ~ c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f61,axiom,
    ! [X3,X0,X6,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3
      | ~ c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_0) ).

fof(f1750,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f60,f1748]) ).

fof(f1748,plain,
    ( spl0_221
  <=> ! [X4,X0,X12,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X4
        | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,X3,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f60,axiom,
    ! [X3,X0,X4,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X4
      | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,X3,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).

fof(f1746,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f59,f1744]) ).

fof(f1744,plain,
    ( spl0_220
  <=> ! [X4,X0,X12,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3
        | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,X3,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f59,axiom,
    ! [X3,X0,X4,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X3
      | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,X3,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).

fof(f1742,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f43,f1740]) ).

fof(f1740,plain,
    ( spl0_219
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f43,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

fof(f1738,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f42,f1736]) ).

fof(f1736,plain,
    ( spl0_218
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f42,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

fof(f1730,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f29,f1728]) ).

fof(f1728,plain,
    ( spl0_217
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X7
        | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f29,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X7
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).

fof(f1726,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f28,f1724]) ).

fof(f1724,plain,
    ( spl0_216
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X7
        | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f28,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X7
      | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).

fof(f1722,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f17,f1720]) ).

fof(f1720,plain,
    ( spl0_215
  <=> ! [X5,X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_Polynomial_OpCons(X5,X1,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f17,axiom,
    ! [X0,X1,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
      | c_Polynomial_OpCons(X5,X1,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).

fof(f1667,plain,
    ( ~ spl0_29
    | spl0_214
    | ~ spl0_99
    | ~ spl0_118 ),
    inference(avatar_split_clause,[],[f1327,f990,f869,f1665,f583]) ).

fof(f583,plain,
    ( spl0_29
  <=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f1665,plain,
    ( spl0_214
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f869,plain,
    ( spl0_99
  <=> ! [X0,X21,X7] :
        ( ~ class_Ring__and__Field_Odvd(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X21,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f990,plain,
    ( spl0_118
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1327,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
    | ~ spl0_99
    | ~ spl0_118 ),
    inference(superposition,[],[f870,f991]) ).

fof(f991,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f990]) ).

fof(f870,plain,
    ( ! [X21,X0,X7] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X21,X0),X0)
        | ~ class_Ring__and__Field_Odvd(X0) )
    | ~ spl0_99 ),
    inference(avatar_component_clause,[],[f869]) ).

fof(f1623,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f352,f1621]) ).

fof(f1621,plain,
    ( spl0_213
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X2,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f352,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X2,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

fof(f1619,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f259,f1617]) ).

fof(f1617,plain,
    ( spl0_212
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f259,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X7,X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

fof(f1615,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f258,f1613]) ).

fof(f1613,plain,
    ( spl0_211
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X5,X0) = X7
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f258,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X5,X0) = X7
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).

fof(f1611,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f232,f1609]) ).

fof(f1609,plain,
    ( spl0_210
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f232,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

fof(f1607,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f220,f1605]) ).

fof(f1605,plain,
    ( spl0_209
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f220,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).

fof(f1594,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f219,f1592]) ).

fof(f1592,plain,
    ( spl0_208
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X7
        | c_HOL_Oplus__class_Oplus(X7,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f219,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X7
      | c_HOL_Oplus__class_Oplus(X7,X5,X0) != c_HOL_Oplus__class_Oplus(X2,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f1590,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f218,f1588]) ).

fof(f1588,plain,
    ( spl0_207
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X2 = X7
        | c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f218,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X2 = X7
      | c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f1586,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f217,f1584]) ).

fof(f1584,plain,
    ( spl0_206
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X2 = X7
        | c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f217,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X2 = X7
      | c_HOL_Oplus__class_Oplus(X5,X7,X0) != c_HOL_Oplus__class_Oplus(X5,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f1582,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f172,f1580]) ).

fof(f1580,plain,
    ( spl0_205
  <=> ! [X6,X0,X12] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X6 = X12
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X6,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f172,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X6 = X12
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X6,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

fof(f1578,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f161,f1576]) ).

fof(f1576,plain,
    ( spl0_204
  <=> ! [X31,X0,X6,X30] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X30 = X31
        | c_HOL_Ominus__class_Ominus(X6,X6,X0) != c_HOL_Ominus__class_Ominus(X30,X31,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f161,axiom,
    ! [X31,X0,X6,X30] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X30 = X31
      | c_HOL_Ominus__class_Ominus(X6,X6,X0) != c_HOL_Ominus__class_Ominus(X30,X31,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

fof(f1574,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f141,f1572]) ).

fof(f1572,plain,
    ( spl0_203
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X0)),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f141,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X6,tc_Polynomial_Opoly(X0)),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__left_0) ).

fof(f1570,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f140,f1568]) ).

fof(f1568,plain,
    ( spl0_202
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(X6,c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f140,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(X6,c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__right_0) ).

fof(f1566,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f120,f1564]) ).

fof(f1564,plain,
    ( spl0_201
  <=> ! [X5,X0,X6] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Oplus__class_Oplus(X6,X5,X0) != X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f120,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Oplus__class_Oplus(X6,X5,X0) != X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

fof(f1562,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f106,f1560]) ).

fof(f1560,plain,
    ( spl0_200
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f106,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I1_J_0) ).

fof(f1558,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f51,f1556]) ).

fof(f1556,plain,
    ( spl0_199
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f51,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X5,X7,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

fof(f1544,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f50,f1542]) ).

fof(f1542,plain,
    ( spl0_198
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) = c_Divides_Odiv__class_Omod(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f50,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X7,X5,X0),X7,X0) = c_Divides_Odiv__class_Omod(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

fof(f1540,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f40,f1538]) ).

fof(f1538,plain,
    ( spl0_197
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f40,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).

fof(f1536,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f39,f1534]) ).

fof(f1534,plain,
    ( spl0_196
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f39,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X7,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

fof(f1532,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f38,f1530]) ).

fof(f1530,plain,
    ( spl0_195
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f38,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

fof(f1528,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f19,f1526]) ).

fof(f1526,plain,
    ( spl0_194
  <=> ! [X5,X0,X3,X1,X7] :
        ( ~ class_HOL_Ozero(X0)
        | X1 = X3
        | c_Polynomial_OpCons(X5,X1,X0) != c_Polynomial_OpCons(X7,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f19,axiom,
    ! [X3,X0,X1,X7,X5] :
      ( ~ class_HOL_Ozero(X0)
      | X1 = X3
      | c_Polynomial_OpCons(X5,X1,X0) != c_Polynomial_OpCons(X7,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).

fof(f1524,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f18,f1522]) ).

fof(f1522,plain,
    ( spl0_193
  <=> ! [X1,X0,X5,X3,X7] :
        ( ~ class_HOL_Ozero(X0)
        | X5 = X7
        | c_Polynomial_OpCons(X5,X1,X0) != c_Polynomial_OpCons(X7,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f18,axiom,
    ! [X3,X0,X1,X7,X5] :
      ( ~ class_HOL_Ozero(X0)
      | X5 = X7
      | c_Polynomial_OpCons(X5,X1,X0) != c_Polynomial_OpCons(X7,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).

fof(f1520,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f15,f1518]) ).

fof(f1518,plain,
    ( spl0_192
  <=> ! [X5,X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Polynomial_OpCons(X5,X1,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f15,axiom,
    ! [X0,X1,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_Polynomial_OpCons(X5,X1,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).

fof(f1493,plain,
    ( spl0_191
    | ~ spl0_185 ),
    inference(avatar_split_clause,[],[f1461,f1387,f1491]) ).

fof(f1491,plain,
    ( spl0_191
  <=> ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1387,plain,
    ( spl0_185
  <=> ! [X0,X21,X35] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X35,X21,X0)
        | c_HOL_Oabs__class_Oabs(X35,X0) != c_HOL_Oabs__class_Oabs(X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f1461,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
        | ~ class_Ring__and__Field_Oordered__idom(X1) )
    | ~ spl0_185 ),
    inference(equality_resolution,[],[f1388]) ).

fof(f1388,plain,
    ( ! [X21,X0,X35] :
        ( c_HOL_Oabs__class_Oabs(X35,X0) != c_HOL_Oabs__class_Oabs(X21,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X35,X21,X0)
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1387]) ).

fof(f1409,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f354,f1407]) ).

fof(f1407,plain,
    ( spl0_190
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f354,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).

fof(f1405,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f350,f1403]) ).

fof(f1403,plain,
    ( spl0_189
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f350,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

fof(f1401,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f349,f1399]) ).

fof(f1399,plain,
    ( spl0_188
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f349,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

fof(f1397,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f348,f1395]) ).

fof(f1395,plain,
    ( spl0_187
  <=> ! [X0,X5,X2,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f348,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X2,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

fof(f1393,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f347,f1391]) ).

fof(f1391,plain,
    ( spl0_186
  <=> ! [X5,X2,X0,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X7,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f347,axiom,
    ! [X2,X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X7,X2,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X7,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

fof(f1389,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f309,f1387]) ).

fof(f309,axiom,
    ! [X21,X0,X35] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X35,X21,X0)
      | c_HOL_Oabs__class_Oabs(X35,X0) != c_HOL_Oabs__class_Oabs(X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).

fof(f1385,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f284,f1383]) ).

fof(f1383,plain,
    ( spl0_184
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f284,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

fof(f1381,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f283,f1379]) ).

fof(f1379,plain,
    ( spl0_183
  <=> ! [X0,X12,X19] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X19,X0),c_HOL_Oplus__class_Oplus(X12,X19,X0),X0) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f283,axiom,
    ! [X0,X19,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X19,X0),c_HOL_Oplus__class_Oplus(X12,X19,X0),X0) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

fof(f1377,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f272,f1375]) ).

fof(f1375,plain,
    ( spl0_182
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f272,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).

fof(f1373,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f271,f1371]) ).

fof(f1371,plain,
    ( spl0_181
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f271,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).

fof(f1369,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f233,f1367]) ).

fof(f1367,plain,
    ( spl0_180
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f233,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).

fof(f1365,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f222,f1363]) ).

fof(f1363,plain,
    ( spl0_179
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X7,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f222,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X7,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).

fof(f1361,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f221,f1359]) ).

fof(f1359,plain,
    ( spl0_178
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X7,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f221,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X7,X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X7,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).

fof(f1357,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f212,f1355]) ).

fof(f1355,plain,
    ( spl0_177
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f212,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

fof(f1353,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f211,f1351]) ).

fof(f1351,plain,
    ( spl0_176
  <=> ! [X6,X0,X12] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ominus__class_Ominus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f211,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ominus__class_Ominus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

fof(f1349,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f210,f1347]) ).

fof(f1347,plain,
    ( spl0_175
  <=> ! [X6,X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f210,axiom,
    ! [X0,X6,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).

fof(f1345,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f208,f1343]) ).

fof(f1343,plain,
    ( spl0_174
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X7,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f208,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X7,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

fof(f1341,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f186,f1339]) ).

fof(f1339,plain,
    ( spl0_173
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f186,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

fof(f1337,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f71,f1335]) ).

fof(f1335,plain,
    ( spl0_172
  <=> ! [X6,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f71,axiom,
    ! [X0,X6] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

fof(f1333,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f52,f1331]) ).

fof(f1331,plain,
    ( spl0_171
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0),X0) = X7 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f52,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X7,X0),X0) = X7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

fof(f1326,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f48,f1324]) ).

fof(f1324,plain,
    ( spl0_170
  <=> ! [X4,X0,X6,X3] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X4 = X6
        | ~ c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f48,axiom,
    ! [X3,X0,X6,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X4 = X6
      | ~ c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).

fof(f1322,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f46,f1320]) ).

fof(f1320,plain,
    ( spl0_169
  <=> ! [X5,X0,X17] :
        ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X17,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f46,axiom,
    ! [X0,X17,X5] :
      ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X5,X17,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

fof(f1318,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f16,f1316]) ).

fof(f1316,plain,
    ( spl0_168
  <=> ! [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_168])]) ).

fof(f16,axiom,
    ! [X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).

fof(f1258,plain,
    ( ~ spl0_29
    | spl0_167
    | ~ spl0_99
    | ~ spl0_102 ),
    inference(avatar_split_clause,[],[f1221,f921,f869,f1256,f583]) ).

fof(f1256,plain,
    ( spl0_167
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f921,plain,
    ( spl0_102
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f1221,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
    | ~ spl0_99
    | ~ spl0_102 ),
    inference(superposition,[],[f870,f922]) ).

fof(f922,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f921]) ).

fof(f1251,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f334,f1249]) ).

fof(f1249,plain,
    ( spl0_166
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f334,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).

fof(f1247,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f333,f1245]) ).

fof(f1245,plain,
    ( spl0_165
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f333,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Ouminus__class_Ouminus(X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).

fof(f1243,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f332,f1241]) ).

fof(f1241,plain,
    ( spl0_164
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X6,X0),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f332,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X6,X0),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).

fof(f1239,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f331,f1237]) ).

fof(f1237,plain,
    ( spl0_163
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X6,X0),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f331,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X12,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X6,X0),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).

fof(f1235,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f322,f1233]) ).

fof(f1233,plain,
    ( spl0_162
  <=> ! [X0,X21,X28] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X28,X0),X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f322,axiom,
    ! [X21,X28,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X28,X0),X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).

fof(f1231,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f321,f1229]) ).

fof(f1229,plain,
    ( spl0_161
  <=> ! [X0,X21,X28] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X28,X0),X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f321,axiom,
    ! [X21,X28,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X28,X0),X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).

fof(f1227,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f320,f1225]) ).

fof(f1225,plain,
    ( spl0_160
  <=> ! [X0,X21,X28] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,c_HOL_Oabs__class_Oabs(X21,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f320,axiom,
    ! [X21,X28,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,c_HOL_Oabs__class_Oabs(X21,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).

fof(f1220,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f319,f1218]) ).

fof(f1218,plain,
    ( spl0_159
  <=> ! [X0,X21,X28] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X28,c_HOL_Oabs__class_Oabs(X21,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f319,axiom,
    ! [X21,X28,X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X28,X21,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X28,c_HOL_Oabs__class_Oabs(X21,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).

fof(f1216,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f312,f1214]) ).

fof(f1214,plain,
    ( spl0_158
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f312,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).

fof(f1212,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f311,f1210]) ).

fof(f1210,plain,
    ( spl0_157
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f311,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).

fof(f1208,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f300,f1206]) ).

fof(f1206,plain,
    ( spl0_156
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f300,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

fof(f1204,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f299,f1202]) ).

fof(f1202,plain,
    ( spl0_155
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f299,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

fof(f1200,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f298,f1198]) ).

fof(f1198,plain,
    ( spl0_154
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f298,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).

fof(f1196,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f291,f1194]) ).

fof(f1194,plain,
    ( spl0_153
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f291,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).

fof(f1192,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f248,f1190]) ).

fof(f1190,plain,
    ( spl0_152
  <=> ! [X5,X0,X7] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f248,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X5,X7,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).

fof(f1188,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f241,f1186]) ).

fof(f1186,plain,
    ( spl0_151
  <=> ! [X6,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f241,axiom,
    ! [X0,X6] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(X6,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).

fof(f1184,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f171,f1182]) ).

fof(f1182,plain,
    ( spl0_150
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X5 = X7
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f171,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X5 = X7
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

fof(f1180,plain,
    ( spl0_149
    | ~ spl0_8
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f918,f857,f478,f1178]) ).

fof(f1178,plain,
    ( spl0_149
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f857,plain,
    ( spl0_96
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f918,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_8
    | ~ spl0_96 ),
    inference(resolution,[],[f858,f480]) ).

fof(f858,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f857]) ).

fof(f1176,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f170,f1174]) ).

fof(f1174,plain,
    ( spl0_148
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X5 = X7
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f170,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X5 = X7
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

fof(f1172,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f156,f1170]) ).

fof(f1170,plain,
    ( spl0_147
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f156,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

fof(f1168,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f34,f1166]) ).

fof(f1166,plain,
    ( spl0_146
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X5 = X7
        | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f34,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X5 = X7
      | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

fof(f1145,plain,
    ( spl0_145
    | ~ spl0_24
    | ~ spl0_94 ),
    inference(avatar_split_clause,[],[f915,f849,f558,f1142]) ).

fof(f1142,plain,
    ( spl0_145
  <=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f558,plain,
    ( spl0_24
  <=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f849,plain,
    ( spl0_94
  <=> ! [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_94])]) ).

fof(f915,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_24
    | ~ spl0_94 ),
    inference(resolution,[],[f850,f560]) ).

fof(f560,plain,
    ( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f558]) ).

fof(f850,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_94 ),
    inference(avatar_component_clause,[],[f849]) ).

fof(f1121,plain,
    ( spl0_144
    | ~ spl0_24
    | ~ spl0_90 ),
    inference(avatar_split_clause,[],[f910,f833,f558,f1119]) ).

fof(f1119,plain,
    ( spl0_144
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f833,plain,
    ( spl0_90
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f910,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_24
    | ~ spl0_90 ),
    inference(resolution,[],[f834,f560]) ).

fof(f834,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 )
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f833]) ).

fof(f1107,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f330,f1105]) ).

fof(f1105,plain,
    ( spl0_143
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f330,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

fof(f1103,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f294,f1101]) ).

fof(f1101,plain,
    ( spl0_142
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f294,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).

fof(f1099,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f293,f1097]) ).

fof(f1097,plain,
    ( spl0_141
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f293,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).

fof(f1095,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f287,f1093]) ).

fof(f1093,plain,
    ( spl0_140
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(X12,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f287,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X6,X12,X0) = c_Polynomial_Opoly__gcd(X12,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).

fof(f1091,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f246,f1089]) ).

fof(f1089,plain,
    ( spl0_139
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f246,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,X7,X0) = c_HOL_Oplus__class_Oplus(X7,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f1087,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f245,f1085]) ).

fof(f1085,plain,
    ( spl0_138
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X12,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f245,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X6,X12,X0) = c_HOL_Oplus__class_Oplus(X12,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f1083,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f236,f1081]) ).

fof(f1081,plain,
    ( spl0_137
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f236,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).

fof(f1079,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f215,f1077]) ).

fof(f1077,plain,
    ( spl0_136
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f215,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X5,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).

fof(f1075,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f201,f1073]) ).

fof(f1073,plain,
    ( spl0_135
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f201,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,X0),X7,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

fof(f1071,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f196,f1069]) ).

fof(f1069,plain,
    ( spl0_134
  <=> ! [X6,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X0),X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f196,axiom,
    ! [X0,X6] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Oplus__class_Oplus(X6,c_HOL_Ozero__class_Ozero(X0),X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f1067,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f192,f1065]) ).

fof(f1065,plain,
    ( spl0_133
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f192,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).

fof(f1063,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f191,f1061]) ).

fof(f1061,plain,
    ( spl0_132
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f191,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,tc_Polynomial_Opoly(X0)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).

fof(f1059,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f168,f1057]) ).

fof(f1057,plain,
    ( spl0_131
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f168,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).

fof(f1055,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f167,f1053]) ).

fof(f1053,plain,
    ( spl0_130
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f167,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

fof(f1051,plain,
    ( spl0_129
    | ~ spl0_23
    | ~ spl0_85 ),
    inference(avatar_split_clause,[],[f896,f813,f553,f1049]) ).

fof(f1049,plain,
    ( spl0_129
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f553,plain,
    ( spl0_23
  <=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f813,plain,
    ( spl0_85
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f896,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_23
    | ~ spl0_85 ),
    inference(resolution,[],[f814,f555]) ).

fof(f555,plain,
    ( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f553]) ).

fof(f814,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f813]) ).

fof(f1047,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f166,f1045]) ).

fof(f1045,plain,
    ( spl0_128
  <=> ! [X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f166,axiom,
    ! [X0,X7] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X7,X0),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).

fof(f1043,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f142,f1041]) ).

fof(f1041,plain,
    ( spl0_127
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X6,X12,X0) = c_HOL_Otimes__class_Otimes(X12,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f142,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X6,X12,X0) = c_HOL_Otimes__class_Otimes(X12,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

fof(f1039,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f139,f1037]) ).

fof(f1037,plain,
    ( spl0_126
  <=> ! [X5,X0,X7] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X7,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f139,axiom,
    ! [X0,X7,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X7,X0),X7,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

fof(f1035,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f118,f1033]) ).

fof(f1033,plain,
    ( spl0_125
  <=> ! [X6,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X6,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f118,axiom,
    ! [X0,X6] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X6,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

fof(f1031,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f113,f1029]) ).

fof(f1029,plain,
    ( spl0_124
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f113,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).

fof(f1027,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f105,f1025]) ).

fof(f1025,plain,
    ( spl0_123
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f105,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

fof(f1023,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f91,f1021]) ).

fof(f1021,plain,
    ( spl0_122
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f91,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f1019,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f4,f1017]) ).

fof(f1017,plain,
    ( spl0_121
  <=> ! [X6,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f4,axiom,
    ! [X0,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).

fof(f1015,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f3,f1013]) ).

fof(f1013,plain,
    ( spl0_120
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) = c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f3,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X5,X0) = c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).

fof(f1011,plain,
    ( spl0_119
    | ~ spl0_23
    | ~ spl0_84 ),
    inference(avatar_split_clause,[],[f894,f809,f553,f1009]) ).

fof(f1009,plain,
    ( spl0_119
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f809,plain,
    ( spl0_84
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f894,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_23
    | ~ spl0_84 ),
    inference(resolution,[],[f810,f555]) ).

fof(f810,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f809]) ).

fof(f992,plain,
    ( spl0_118
    | ~ spl0_21
    | ~ spl0_79 ),
    inference(avatar_split_clause,[],[f885,f789,f543,f990]) ).

fof(f789,plain,
    ( spl0_79
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f885,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_21
    | ~ spl0_79 ),
    inference(resolution,[],[f790,f545]) ).

fof(f790,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 )
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f789]) ).

fof(f983,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f317,f981]) ).

fof(f981,plain,
    ( spl0_117
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X6,X12,X0),X12,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f317,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X6,X12,X0),X12,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).

fof(f979,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f316,f977]) ).

fof(f977,plain,
    ( spl0_116
  <=> ! [X6,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X6,X12,X0),X6,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f316,axiom,
    ! [X0,X6,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X6,X12,X0),X6,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).

fof(f975,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f281,f973]) ).

fof(f973,plain,
    ( spl0_115
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f281,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

fof(f971,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f277,f969]) ).

fof(f969,plain,
    ( spl0_114
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f277,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

fof(f967,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f276,f965]) ).

fof(f965,plain,
    ( spl0_113
  <=> ! [X0,X7] :
        ( ~ 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),X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f276,axiom,
    ! [X0,X7] :
      ( ~ 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),X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

fof(f963,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f275,f961]) ).

fof(f961,plain,
    ( spl0_112
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f275,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f959,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f274,f957]) ).

fof(f957,plain,
    ( spl0_111
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f274,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f955,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f269,f953]) ).

fof(f953,plain,
    ( spl0_110
  <=> ! [X5,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f269,axiom,
    ! [X0,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

fof(f951,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f267,f949]) ).

fof(f949,plain,
    ( spl0_109
  <=> ! [X0,X12] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f267,axiom,
    ! [X0,X12] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

fof(f947,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f266,f945]) ).

fof(f266,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f943,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f265,f941]) ).

fof(f265,axiom,
    ! [X0,X5] :
      ( ~ 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),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

fof(f939,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f224,f937]) ).

fof(f224,axiom,
    ! [X0,X17] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X17,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

fof(f935,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f134,f933]) ).

fof(f933,plain,
    ( spl0_105
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f134,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

fof(f931,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f111,f929]) ).

fof(f929,plain,
    ( spl0_104
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f111,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).

fof(f927,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f110,f925]) ).

fof(f925,plain,
    ( spl0_103
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f110,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).

fof(f923,plain,
    ( spl0_102
    | ~ spl0_21
    | ~ spl0_78 ),
    inference(avatar_split_clause,[],[f879,f785,f543,f921]) ).

fof(f785,plain,
    ( spl0_78
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f879,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_21
    | ~ spl0_78 ),
    inference(resolution,[],[f786,f545]) ).

fof(f786,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f785]) ).

fof(f907,plain,
    ( spl0_101
    | ~ spl0_24
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f875,f777,f558,f905]) ).

fof(f905,plain,
    ( spl0_101
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f777,plain,
    ( spl0_76
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f875,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_24
    | ~ spl0_76 ),
    inference(resolution,[],[f778,f560]) ).

fof(f778,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f777]) ).

fof(f884,plain,
    ( spl0_100
    | ~ spl0_18
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f873,f773,f528,f882]) ).

fof(f882,plain,
    ( spl0_100
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f528,plain,
    ( spl0_18
  <=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f773,plain,
    ( spl0_75
  <=> ! [X6,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X6,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f873,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
    | ~ spl0_18
    | ~ spl0_75 ),
    inference(resolution,[],[f774,f530]) ).

fof(f530,plain,
    ( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f528]) ).

fof(f774,plain,
    ( ! [X0,X6] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X6,X6,X0) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f773]) ).

fof(f871,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f365,f869]) ).

fof(f365,axiom,
    ! [X21,X0,X7] :
      ( ~ class_Ring__and__Field_Odvd(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X7,c_HOL_Otimes__class_Otimes(X7,X21,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).

fof(f867,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f364,f865]) ).

fof(f865,plain,
    ( spl0_98
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f364,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

fof(f863,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f363,f861]) ).

fof(f861,plain,
    ( spl0_97
  <=> ! [X5,X0,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f363,axiom,
    ! [X0,X7,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X7,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

fof(f859,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f338,f857]) ).

fof(f338,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).

fof(f855,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f290,f853]) ).

fof(f853,plain,
    ( spl0_95
  <=> ! [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_95])]) ).

fof(f290,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

fof(f851,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f289,f849]) ).

fof(f289,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).

fof(f847,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f243,f845]) ).

fof(f845,plain,
    ( spl0_93
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f243,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

fof(f843,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f242,f841]) ).

fof(f841,plain,
    ( spl0_92
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f242,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

fof(f839,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f207,f837]) ).

fof(f837,plain,
    ( spl0_91
  <=> ! [X5,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Odiv(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f207,axiom,
    ! [X0,X5] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Odiv(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).

fof(f835,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f206,f833]) ).

fof(f206,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

fof(f831,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f200,f829]) ).

fof(f829,plain,
    ( spl0_89
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f200,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(f827,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f199,f825]) ).

fof(f825,plain,
    ( spl0_88
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f199,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f823,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f198,f821]) ).

fof(f821,plain,
    ( spl0_87
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f198,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f819,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f195,f817]) ).

fof(f817,plain,
    ( spl0_86
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f195,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f815,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f194,f813]) ).

fof(f194,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f811,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f193,f809]) ).

fof(f193,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f807,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f146,f805]) ).

fof(f805,plain,
    ( spl0_83
  <=> ! [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_83])]) ).

fof(f146,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).

fof(f803,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f131,f801]) ).

fof(f801,plain,
    ( spl0_82
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f131,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f799,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f130,f797]) ).

fof(f797,plain,
    ( spl0_81
  <=> ! [X6,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X6,X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f130,axiom,
    ! [X0,X6] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X6,X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

fof(f795,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f129,f793]) ).

fof(f793,plain,
    ( spl0_80
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f129,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f791,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f128,f789]) ).

fof(f128,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f787,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f127,f785]) ).

fof(f127,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f783,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f117,f781]) ).

fof(f781,plain,
    ( spl0_77
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f117,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

fof(f779,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f116,f777]) ).

fof(f116,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

fof(f775,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f114,f773]) ).

fof(f114,axiom,
    ! [X0,X6] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X6,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

fof(f771,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f94,f769]) ).

fof(f769,plain,
    ( spl0_74
  <=> ! [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_74])]) ).

fof(f94,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).

fof(f767,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f373,f764]) ).

fof(f764,plain,
    ( spl0_73
  <=> c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f373,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

fof(f762,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f351,f760]) ).

fof(f760,plain,
    ( spl0_72
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f351,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).

fof(f758,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f323,f756]) ).

fof(f756,plain,
    ( spl0_71
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f323,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

fof(f754,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f27,f752]) ).

fof(f752,plain,
    ( spl0_70
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f27,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

fof(f750,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f353,f748]) ).

fof(f748,plain,
    ( spl0_69
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f353,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

fof(f746,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f441,f744]) ).

fof(f744,plain,
    ( spl0_68
  <=> ! [X36] :
        ( ~ class_HOL_Ozero(X36)
        | class_HOL_Ozero(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f441,axiom,
    ! [X36] :
      ( ~ class_HOL_Ozero(X36)
      | class_HOL_Ozero(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).

fof(f742,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f440,f740]) ).

fof(f740,plain,
    ( spl0_67
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_Power_Opower(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f440,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_Power_Opower(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).

fof(f738,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f439,f736]) ).

fof(f736,plain,
    ( spl0_66
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
        | class_Int_Onumber__ring(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f439,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
      | class_Int_Onumber__ring(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

fof(f734,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f438,f732]) ).

fof(f732,plain,
    ( spl0_65
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ofield(X36)
        | class_Divides_Oring__div(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f438,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ofield(X36)
      | class_Divides_Oring__div(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).

fof(f730,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f437,f728]) ).

fof(f728,plain,
    ( spl0_64
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f437,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).

fof(f726,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f436,f724]) ).

fof(f724,plain,
    ( spl0_63
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oidom(X36)
        | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f436,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).

fof(f722,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f435,f720]) ).

fof(f720,plain,
    ( spl0_62
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X36)
        | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f435,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X36)
      | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).

fof(f718,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f434,f716]) ).

fof(f716,plain,
    ( spl0_61
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ofield(X36)
        | class_Divides_Osemiring__div(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f434,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ofield(X36)
      | class_Divides_Osemiring__div(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).

fof(f714,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f433,f712]) ).

fof(f712,plain,
    ( spl0_60
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
        | class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f433,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
      | class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).

fof(f710,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f432,f708]) ).

fof(f708,plain,
    ( spl0_59
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Oab__group__add(X36)
        | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f432,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Oab__group__add(X36)
      | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).

fof(f706,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f431,f704]) ).

fof(f704,plain,
    ( spl0_58
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
        | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f431,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
      | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).

fof(f702,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f430,f700]) ).

fof(f700,plain,
    ( spl0_57
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
        | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f430,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
      | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).

fof(f698,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f429,f696]) ).

fof(f696,plain,
    ( spl0_56
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f429,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).

fof(f694,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f428,f692]) ).

fof(f692,plain,
    ( spl0_55
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X36)
        | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f428,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X36)
      | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).

fof(f690,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f427,f688]) ).

fof(f688,plain,
    ( spl0_54
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
        | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f427,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
      | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).

fof(f686,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f426,f684]) ).

fof(f684,plain,
    ( spl0_53
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Oab__group__add(X36)
        | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f426,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Oab__group__add(X36)
      | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).

fof(f682,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f425,f680]) ).

fof(f680,plain,
    ( spl0_52
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
        | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f425,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X36)
      | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).

fof(f678,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f424,f676]) ).

fof(f676,plain,
    ( spl0_51
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oordered__idom(X36)
        | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f424,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oordered__idom(X36)
      | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).

fof(f674,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f423,f672]) ).

fof(f672,plain,
    ( spl0_50
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f423,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).

fof(f670,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f422,f668]) ).

fof(f668,plain,
    ( spl0_49
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
        | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f422,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
      | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).

fof(f666,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f421,f664]) ).

fof(f664,plain,
    ( spl0_48
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
        | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f421,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
      | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).

fof(f662,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f420,f660]) ).

fof(f660,plain,
    ( spl0_47
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
        | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f420,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X36)
      | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).

fof(f658,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f419,f656]) ).

fof(f656,plain,
    ( spl0_46
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f419,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).

fof(f654,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f418,f652]) ).

fof(f652,plain,
    ( spl0_45
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
        | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f418,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
      | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).

fof(f650,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f417,f648]) ).

fof(f648,plain,
    ( spl0_44
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
        | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f417,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X36)
      | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

fof(f646,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f416,f644]) ).

fof(f644,plain,
    ( spl0_43
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
        | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f416,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X36)
      | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

fof(f642,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f415,f640]) ).

fof(f640,plain,
    ( spl0_42
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oidom(X36)
        | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f415,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).

fof(f638,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f414,f636]) ).

fof(f636,plain,
    ( spl0_41
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
        | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f414,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
      | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).

fof(f634,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f413,f632]) ).

fof(f632,plain,
    ( spl0_40
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oordered__idom(X36)
        | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f413,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oordered__idom(X36)
      | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).

fof(f630,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f412,f628]) ).

fof(f628,plain,
    ( spl0_39
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oordered__idom(X36)
        | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f412,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oordered__idom(X36)
      | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).

fof(f626,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f411,f624]) ).

fof(f624,plain,
    ( spl0_38
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f411,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f622,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f410,f620]) ).

fof(f620,plain,
    ( spl0_37
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oidom(X36)
        | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f410,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f618,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f409,f616]) ).

fof(f616,plain,
    ( spl0_36
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oordered__idom(X36)
        | class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f409,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oordered__idom(X36)
      | class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).

fof(f614,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f408,f612]) ).

fof(f612,plain,
    ( spl0_35
  <=> ! [X36] :
        ( ~ class_Ring__and__Field_Oidom(X36)
        | class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f408,axiom,
    ! [X36] :
      ( ~ class_Ring__and__Field_Oidom(X36)
      | class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).

fof(f610,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f376,f608]) ).

fof(f608,plain,
    ( spl0_34
  <=> ! [X36] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
        | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f376,axiom,
    ! [X36] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X36)
      | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X36)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f606,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f374,f603]) ).

fof(f374,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

fof(f601,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f407,f598]) ).

fof(f598,plain,
    ( spl0_32
  <=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f407,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

fof(f596,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f406,f593]) ).

fof(f593,plain,
    ( spl0_31
  <=> class_Power_Opower(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f406,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

fof(f591,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f405,f588]) ).

fof(f588,plain,
    ( spl0_30
  <=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f405,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(f586,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f404,f583]) ).

fof(f404,axiom,
    class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).

fof(f581,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f403,f578]) ).

fof(f578,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f403,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

fof(f576,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f402,f573]) ).

fof(f573,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f402,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

fof(f571,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f401,f568]) ).

fof(f568,plain,
    ( spl0_26
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f401,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f566,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f400,f563]) ).

fof(f563,plain,
    ( spl0_25
  <=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f400,axiom,
    class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

fof(f561,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f399,f558]) ).

fof(f399,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

fof(f556,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f398,f553]) ).

fof(f398,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

fof(f551,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f397,f548]) ).

fof(f548,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f397,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

fof(f546,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f396,f543]) ).

fof(f396,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

fof(f541,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f395,f538]) ).

fof(f538,plain,
    ( spl0_20
  <=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f395,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).

fof(f536,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f394,f533]) ).

fof(f533,plain,
    ( spl0_19
  <=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f394,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

fof(f531,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f393,f528]) ).

fof(f393,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

fof(f526,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f392,f523]) ).

fof(f523,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f392,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

fof(f521,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f391,f518]) ).

fof(f518,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f391,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

fof(f516,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f390,f513]) ).

fof(f513,plain,
    ( spl0_15
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f390,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

fof(f511,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f389,f508]) ).

fof(f508,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f389,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

fof(f506,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f388,f503]) ).

fof(f503,plain,
    ( spl0_13
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f388,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

fof(f501,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f387,f498]) ).

fof(f498,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f387,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

fof(f496,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f386,f493]) ).

fof(f493,plain,
    ( spl0_11
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f386,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

fof(f491,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f385,f488]) ).

fof(f488,plain,
    ( spl0_10
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f385,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f486,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f384,f483]) ).

fof(f483,plain,
    ( spl0_9
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f384,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

fof(f481,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f383,f478]) ).

fof(f383,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

fof(f476,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f382,f473]) ).

fof(f473,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f382,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

fof(f471,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f381,f468]) ).

fof(f468,plain,
    ( spl0_6
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f381,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

fof(f466,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f380,f463]) ).

fof(f463,plain,
    ( spl0_5
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f380,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f461,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f379,f458]) ).

fof(f458,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f379,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f456,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f378,f453]) ).

fof(f453,plain,
    ( spl0_3
  <=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f378,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

fof(f451,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f377,f448]) ).

fof(f448,plain,
    ( spl0_2
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f377,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f446,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f375,f443]) ).

fof(f375,axiom,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : ALG434-1 : TPTP v8.2.0. Released v4.1.0.
% 0.13/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n011.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 22:47:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (14036)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40  % (14040)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40  % (14042)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.40  % (14041)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.40  % (14043)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.40  % (14037)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.41  % (14038)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.41  % (14039)WARNING: value z3 for option sas not known
% 0.15/0.41  % (14039)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)
% 0.21/0.44  TRYING [1]
% 0.21/0.44  TRYING [2]
% 0.21/0.44  % (14041)First to succeed.
% 0.21/0.45  % (14041)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14036"
% 0.21/0.46  % (14041)Refutation found. Thanks to Tanya!
% 0.21/0.46  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46  % (14041)------------------------------
% 0.21/0.46  % (14041)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46  % (14041)Termination reason: Refutation
% 0.21/0.46  
% 0.21/0.46  % (14041)Memory used [KB]: 1887
% 0.21/0.46  % (14041)Time elapsed: 0.052 s
% 0.21/0.46  % (14041)Instructions burned: 94 (million)
% 0.21/0.46  % (14036)Success in time 0.089 s
%------------------------------------------------------------------------------