TSTP Solution File: ALG439-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG439-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 04:30:35 EDT 2024

% Result   : Unsatisfiable 0.16s 0.43s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  631
% Syntax   : Number of formulae    : 1002 ( 443 unt;   0 def)
%            Number of atoms       : 1806 ( 216 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives : 1309 ( 505   ~; 480   |;   0   &)
%                                         ( 324 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  392 ( 390 usr; 325 prp; 0-3 aty)
%            Number of functors    :   30 (  30 usr;   7 con; 0-3 aty)
%            Number of variables   :  679 ( 679   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2688,plain,
    $false,
    inference(avatar_sat_refutation,[],[f926,f931,f936,f941,f946,f951,f956,f961,f966,f971,f976,f981,f986,f991,f996,f1001,f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1191,f1196,f1201,f1206,f1211,f1216,f1221,f1226,f1231,f1236,f1241,f1246,f1251,f1256,f1261,f1266,f1271,f1276,f1281,f1286,f1291,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1341,f1346,f1351,f1356,f1361,f1366,f1371,f1376,f1381,f1386,f1391,f1396,f1401,f1406,f1411,f1416,f1421,f1426,f1431,f1436,f1441,f1446,f1451,f1456,f1461,f1466,f1471,f1476,f1481,f1486,f1491,f1496,f1501,f1506,f1511,f1516,f1521,f1526,f1531,f1536,f1541,f1546,f1551,f1556,f1561,f1566,f1571,f1576,f1585,f1587,f1595,f1599,f1603,f1607,f1611,f1615,f1619,f1623,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1703,f1707,f1711,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1890,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1939,f1943,f1947,f1951,f1955,f1959,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2015,f2019,f2023,f2027,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2157,f2169,f2173,f2177,f2181,f2185,f2189,f2193,f2197,f2201,f2205,f2209,f2213,f2217,f2221,f2225,f2229,f2233,f2237,f2241,f2245,f2249,f2253,f2257,f2261,f2265,f2273,f2340,f2369,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2403,f2407,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2442,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2491,f2495,f2499,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2589,f2629,f2659,f2684,f2687]) ).

fof(f2687,plain,
    ( spl0_133
    | ~ spl0_132 ),
    inference(avatar_split_clause,[],[f1590,f1578,f1582]) ).

fof(f1582,plain,
    ( spl0_133
  <=> v_c = v_y ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f1578,plain,
    ( spl0_132
  <=> v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f1590,plain,
    ( v_c = v_y
    | ~ spl0_132 ),
    inference(forward_demodulation,[],[f1580,f734]) ).

fof(f734,axiom,
    ! [X7,X4] : c_Polynomial_Opoly(c_Polynomial_OpCons(X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X4,tc_Complex_Ocomplex) = X7,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mpoly__base__conv_I2_J_0) ).

fof(f1580,plain,
    ( v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
    | ~ spl0_132 ),
    inference(avatar_component_clause,[],[f1578]) ).

fof(f2684,plain,
    ( spl0_134
    | ~ spl0_321 ),
    inference(avatar_contradiction_clause,[],[f2683]) ).

fof(f2683,plain,
    ( $false
    | spl0_134
    | ~ spl0_321 ),
    inference(trivial_inequality_removal,[],[f2682]) ).

fof(f2682,plain,
    ( v_c != v_c
    | spl0_134
    | ~ spl0_321 ),
    inference(superposition,[],[f1594,f2542]) ).

fof(f2542,plain,
    ( ! [X7,X4] : c_Polynomial_Opoly(c_Polynomial_OpCons(X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X4,tc_Complex_Ocomplex) = X7
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f2541]) ).

fof(f2541,plain,
    ( spl0_321
  <=> ! [X4,X7] : c_Polynomial_Opoly(c_Polynomial_OpCons(X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X4,tc_Complex_Ocomplex) = X7 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f1594,plain,
    ( v_c != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
    | spl0_134 ),
    inference(avatar_component_clause,[],[f1592]) ).

fof(f1592,plain,
    ( spl0_134
  <=> v_c = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f2659,plain,
    ( spl0_324
    | ~ spl0_30
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2079,f1933,f1068,f2657]) ).

fof(f2657,plain,
    ( spl0_324
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f1068,plain,
    ( spl0_30
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f1933,plain,
    ( spl0_217
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f2079,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
    | ~ spl0_30
    | ~ spl0_217 ),
    inference(resolution,[],[f1934,f1070]) ).

fof(f1070,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f1068]) ).

fof(f1934,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
    | ~ spl0_217 ),
    inference(avatar_component_clause,[],[f1933]) ).

fof(f2629,plain,
    ( spl0_323
    | ~ spl0_84
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2078,f1933,f1338,f2627]) ).

fof(f2627,plain,
    ( spl0_323
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f1338,plain,
    ( spl0_84
  <=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f2078,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
    | ~ spl0_84
    | ~ spl0_217 ),
    inference(resolution,[],[f1934,f1340]) ).

fof(f1340,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
    | ~ spl0_84 ),
    inference(avatar_component_clause,[],[f1338]) ).

fof(f2589,plain,
    ( spl0_322
    | ~ spl0_121
    | ~ spl0_217 ),
    inference(avatar_split_clause,[],[f2077,f1933,f1523,f2587]) ).

fof(f2587,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f1523,plain,
    ( spl0_121
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f2077,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_121
    | ~ spl0_217 ),
    inference(resolution,[],[f1934,f1525]) ).

fof(f1525,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1523]) ).

fof(f2543,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f734,f2541]) ).

fof(f2539,plain,
    ( spl0_320
    | ~ spl0_30
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2075,f1929,f1068,f2537]) ).

fof(f2537,plain,
    ( spl0_320
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f1929,plain,
    ( spl0_216
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f2075,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
    | ~ spl0_30
    | ~ spl0_216 ),
    inference(resolution,[],[f1930,f1070]) ).

fof(f1930,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f1929]) ).

fof(f2535,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f727,f2533]) ).

fof(f2533,plain,
    ( spl0_319
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f727,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__root_1) ).

fof(f2531,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f726,f2529]) ).

fof(f2529,plain,
    ( spl0_318
  <=> ! [X4,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)),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f726,axiom,
    ! [X0,X4] :
      ( ~ 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)),X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__0_0) ).

fof(f2527,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f707,f2525]) ).

fof(f2525,plain,
    ( spl0_317
  <=> ! [X0,X10] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f707,axiom,
    ! [X10,X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X10,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coeff__0_0) ).

fof(f2523,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f706,f2521]) ).

fof(f2521,plain,
    ( spl0_316
  <=> ! [X0,X10] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f706,axiom,
    ! [X10,X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X10,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).

fof(f2519,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f703,f2517]) ).

fof(f2517,plain,
    ( spl0_315
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f703,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).

fof(f2515,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f702,f2513]) ).

fof(f2513,plain,
    ( spl0_314
  <=> ! [X0,X3] :
        ( ~ 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),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f702,axiom,
    ! [X3,X0] :
      ( ~ 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),X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__0__left_0) ).

fof(f2511,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f682,f2509]) ).

fof(f2509,plain,
    ( spl0_313
  <=> ! [X0,X1,X3] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Polynomial_Opos__poly(X3,X0)
        | c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f682,axiom,
    ! [X3,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(X3,X0)
      | c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).

fof(f2507,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f674,f2505]) ).

fof(f2505,plain,
    ( spl0_312
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f674,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).

fof(f2503,plain,
    spl0_311,
    inference(avatar_split_clause,[],[f673,f2501]) ).

fof(f2501,plain,
    ( spl0_311
  <=> ! [X0,X11] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X11,tc_Polynomial_Opoly(X0)) = X11 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).

fof(f673,axiom,
    ! [X0,X11] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X11,tc_Polynomial_Opoly(X0)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).

fof(f2499,plain,
    spl0_310,
    inference(avatar_split_clause,[],[f670,f2497]) ).

fof(f2497,plain,
    ( spl0_310
  <=> ! [X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f670,axiom,
    ! [X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).

fof(f2495,plain,
    ( spl0_309
    | ~ spl0_84
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2074,f1929,f1338,f2493]) ).

fof(f2493,plain,
    ( spl0_309
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f2074,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_84
    | ~ spl0_216 ),
    inference(resolution,[],[f1930,f1340]) ).

fof(f2491,plain,
    ( spl0_307
    | ~ spl0_308 ),
    inference(avatar_split_clause,[],[f648,f2488,f2484]) ).

fof(f2484,plain,
    ( spl0_307
  <=> c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f2488,plain,
    ( spl0_308
  <=> class_OrderedGroup_Olordered__ab__group__add(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f648,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__def__raw_0) ).

fof(f2482,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f635,f2480]) ).

fof(f2480,plain,
    ( spl0_306
  <=> ! [X4,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f635,axiom,
    ! [X0,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(X0),X0) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f2478,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f589,f2476]) ).

fof(f2476,plain,
    ( spl0_305
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oone__class_Oone(X0) = c_Polynomial_Opoly(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f589,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oone__class_Oone(X0) = c_Polynomial_Opoly(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__1_0) ).

fof(f2474,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f571,f2472]) ).

fof(f2472,plain,
    ( spl0_304
  <=> ! [X5,X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X4,X5,X0) = c_Polynomial_Opoly__gcd(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f571,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X4,X5,X0) = c_Polynomial_Opoly__gcd(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).

fof(f2470,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f546,f2468]) ).

fof(f2468,plain,
    ( spl0_303
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).

fof(f546,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X0) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f2466,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f525,f2464]) ).

fof(f2464,plain,
    ( spl0_302
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f525,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

fof(f2462,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f522,f2460]) ).

fof(f2460,plain,
    ( spl0_301
  <=> ! [X4,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f522,axiom,
    ! [X0,X4] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

fof(f2458,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f510,f2456]) ).

fof(f2456,plain,
    ( spl0_300
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f510,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f2454,plain,
    ( spl0_299
    | ~ spl0_121
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f2073,f1929,f1523,f2452]) ).

fof(f2452,plain,
    ( spl0_299
  <=> ! [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_299])]) ).

fof(f2073,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_121
    | ~ spl0_216 ),
    inference(resolution,[],[f1930,f1525]) ).

fof(f2450,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f509,f2448]) ).

fof(f2448,plain,
    ( spl0_298
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f509,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

fof(f2446,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f472,f2444]) ).

fof(f2444,plain,
    ( spl0_297
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f472,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

fof(f2442,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f441,f2440]) ).

fof(f2440,plain,
    ( spl0_296
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f441,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f2438,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f440,f2436]) ).

fof(f2436,plain,
    ( spl0_295
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f440,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0) = c_Lattices_Oupper__semilattice__class_Osup(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f2434,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f417,f2432]) ).

fof(f2432,plain,
    ( spl0_294
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f417,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f2430,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f416,f2428]) ).

fof(f2428,plain,
    ( spl0_293
  <=> ! [X5,X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X4,X5,X0) = c_HOL_Oplus__class_Oplus(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f416,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X4,X5,X0) = c_HOL_Oplus__class_Oplus(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

fof(f2426,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f406,f2424]) ).

fof(f2424,plain,
    ( spl0_292
  <=> ! [X4,X0] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_RealVector_Onorm__class_Onorm(X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f406,axiom,
    ! [X0,X4] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_RealVector_Onorm__class_Onorm(X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).

fof(f2422,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f371,f2420]) ).

fof(f2420,plain,
    ( spl0_291
  <=> ! [X4,X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X4,X0),X4,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f371,axiom,
    ! [X0,X1,X4] :
      ( ~ class_HOL_Ozero(X0)
      | c_Polynomial_Ocoeff(c_Polynomial_Omonom(X1,X4,X0),X4,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_coeff__monom_0) ).

fof(f2418,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f325,f2416]) ).

fof(f2416,plain,
    ( spl0_290
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f325,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__minus_0) ).

fof(f2414,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f324,f2412]) ).

fof(f2412,plain,
    ( spl0_289
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f324,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus_0) ).

fof(f2407,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f323,f2405]) ).

fof(f2405,plain,
    ( spl0_288
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f323,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

fof(f2403,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f320,f2401]) ).

fof(f2401,plain,
    ( spl0_287
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f320,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f2399,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f319,f2397]) ).

fof(f2397,plain,
    ( spl0_286
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f319,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0) = c_Lattices_Olower__semilattice__class_Oinf(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f2395,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f272,f2393]) ).

fof(f2393,plain,
    ( spl0_285
  <=> ! [X5,X4,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X4,X5,X0) = c_HOL_Otimes__class_Otimes(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f272,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X4,X5,X0) = c_HOL_Otimes__class_Otimes(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

fof(f2391,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f265,f2389]) ).

fof(f2389,plain,
    ( spl0_284
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f265,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

fof(f2387,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f216,f2385]) ).

fof(f2385,plain,
    ( spl0_283
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f216,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

fof(f2383,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f202,f2381]) ).

fof(f2381,plain,
    ( spl0_282
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f202,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).

fof(f2379,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f83,f2377]) ).

fof(f2377,plain,
    ( spl0_281
  <=> ! [X6,X19] :
        ( X6 = X19
        | ~ c_lessequals(X6,X19,tc_RealDef_Oreal)
        | ~ c_lessequals(X19,X6,tc_RealDef_Oreal) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f83,axiom,
    ! [X6,X19] :
      ( X6 = X19
      | ~ c_lessequals(X6,X19,tc_RealDef_Oreal)
      | ~ c_lessequals(X19,X6,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).

fof(f2375,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f71,f2373]) ).

fof(f2373,plain,
    ( spl0_280
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f71,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f2369,plain,
    ( spl0_279
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2361,f2255,f2367]) ).

fof(f2367,plain,
    ( spl0_279
  <=> ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f2255,plain,
    ( spl0_274
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X4,X5,X0)
        | c_lessequals(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2361,plain,
    ( ! [X0,X1] :
        ( c_lessequals(X0,X0,X1)
        | ~ class_Orderings_Olinorder(X1) )
    | ~ spl0_274 ),
    inference(factoring,[],[f2256]) ).

fof(f2256,plain,
    ( ! [X0,X4,X5] :
        ( c_lessequals(X5,X4,X0)
        | c_lessequals(X4,X5,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2255]) ).

fof(f2340,plain,
    ( spl0_278
    | ~ spl0_17
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2071,f1921,f1003,f2338]) ).

fof(f2338,plain,
    ( spl0_278
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f1003,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1921,plain,
    ( spl0_214
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X3,X0) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f2071,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
    | ~ spl0_17
    | ~ spl0_214 ),
    inference(resolution,[],[f1922,f1005]) ).

fof(f1005,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f1003]) ).

fof(f1922,plain,
    ( ! [X3,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X3,X0) = X3 )
    | ~ spl0_214 ),
    inference(avatar_component_clause,[],[f1921]) ).

fof(f2273,plain,
    ( spl0_277
    | ~ spl0_63
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2070,f1921,f1233,f2271]) ).

fof(f2271,plain,
    ( spl0_277
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f1233,plain,
    ( spl0_63
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f2070,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
    | ~ spl0_63
    | ~ spl0_214 ),
    inference(resolution,[],[f1922,f1235]) ).

fof(f1235,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f1233]) ).

fof(f2265,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f634,f2263]) ).

fof(f2263,plain,
    ( spl0_276
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f634,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

fof(f2261,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f633,f2259]) ).

fof(f2259,plain,
    ( spl0_275
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X4,X0)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f633,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X4,X0)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

fof(f2257,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f631,f2255]) ).

fof(f631,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X4,X5,X0)
      | c_lessequals(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

fof(f2253,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f629,f2251]) ).

fof(f2251,plain,
    ( spl0_273
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f629,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

fof(f2249,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f576,f2247]) ).

fof(f2247,plain,
    ( spl0_272
  <=> ! [X5,X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X4,X5,X0),X4,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f576,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X4,X5,X0),X4,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).

fof(f2245,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f575,f2243]) ).

fof(f2243,plain,
    ( spl0_271
  <=> ! [X5,X4,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X4,X5,X0),X5,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f575,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X4,X5,X0),X5,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).

fof(f2241,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f555,f2239]) ).

fof(f2239,plain,
    ( spl0_270
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
        | c_lessequals(X4,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).

fof(f555,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
      | c_lessequals(X4,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

fof(f2237,plain,
    ( spl0_269
    | ~ spl0_107
    | ~ spl0_214 ),
    inference(avatar_split_clause,[],[f2069,f1921,f1453,f2235]) ).

fof(f2235,plain,
    ( spl0_269
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f1453,plain,
    ( spl0_107
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f2069,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_107
    | ~ spl0_214 ),
    inference(resolution,[],[f1922,f1455]) ).

fof(f1455,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1453]) ).

fof(f2233,plain,
    spl0_268,
    inference(avatar_split_clause,[],[f554,f2231]) ).

fof(f2231,plain,
    ( spl0_268
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
        | c_lessequals(X4,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f554,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
      | c_lessequals(X4,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

fof(f2229,plain,
    spl0_267,
    inference(avatar_split_clause,[],[f505,f2227]) ).

fof(f2227,plain,
    ( spl0_267
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).

fof(f505,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f2225,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f503,f2223]) ).

fof(f2223,plain,
    ( spl0_266
  <=> ! [X2,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f503,axiom,
    ! [X2,X0] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

fof(f2221,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f501,f2219]) ).

fof(f2219,plain,
    ( spl0_265
  <=> ! [X4,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f501,axiom,
    ! [X0,X4] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).

fof(f2217,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f500,f2215]) ).

fof(f2215,plain,
    ( spl0_264
  <=> ! [X4,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),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f500,axiom,
    ! [X0,X4] :
      ( ~ 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),X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

fof(f2213,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f499,f2211]) ).

fof(f2211,plain,
    ( spl0_263
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f499,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f2209,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f498,f2207]) ).

fof(f2207,plain,
    ( spl0_262
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f498,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f2205,plain,
    spl0_261,
    inference(avatar_split_clause,[],[f497,f2203]) ).

fof(f2203,plain,
    ( spl0_261
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f497,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

fof(f2201,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f496,f2199]) ).

fof(f2199,plain,
    ( spl0_260
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f496,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

fof(f2197,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f438,f2195]) ).

fof(f2195,plain,
    ( spl0_259
  <=> ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).

fof(f438,axiom,
    ! [X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__0_0) ).

fof(f2193,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f342,f2191]) ).

fof(f2191,plain,
    ( spl0_258
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).

fof(f342,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

fof(f2189,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f298,f2187]) ).

fof(f2187,plain,
    ( spl0_257
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_HOL_Oord__class_Oless(X5,X4,X0)
        | c_lessequals(X4,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f298,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_HOL_Oord__class_Oless(X5,X4,X0)
      | c_lessequals(X4,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

fof(f2185,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f296,f2183]) ).

fof(f2183,plain,
    ( spl0_256
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
        | ~ c_lessequals(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f296,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
      | ~ c_lessequals(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

fof(f2181,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f292,f2179]) ).

fof(f2179,plain,
    ( spl0_255
  <=> ! [X5,X4,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
        | ~ c_lessequals(X5,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f292,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X5,X0)
      | ~ c_lessequals(X5,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

fof(f2177,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f244,f2175]) ).

fof(f2175,plain,
    ( spl0_254
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f244,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_degree__1_0) ).

fof(f2173,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f154,f2171]) ).

fof(f2171,plain,
    ( spl0_253
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f154,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

fof(f2169,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f53,f2167]) ).

fof(f2167,plain,
    ( spl0_252
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f53,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).

fof(f2157,plain,
    ( ~ spl0_37
    | spl0_251
    | ~ spl0_207
    | ~ spl0_225 ),
    inference(avatar_split_clause,[],[f2094,f1965,f1888,f2155,f1103]) ).

fof(f1103,plain,
    ( spl0_37
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f2155,plain,
    ( spl0_251
  <=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f1888,plain,
    ( spl0_207
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f1965,plain,
    ( spl0_225
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f2094,plain,
    ( ! [X0] :
        ( c_lessequals(X0,X0,tc_nat)
        | ~ class_Lattices_Olattice(tc_nat) )
    | ~ spl0_207
    | ~ spl0_225 ),
    inference(superposition,[],[f1966,f1889]) ).

fof(f1889,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f1888]) ).

fof(f1966,plain,
    ( ! [X0,X4,X5] :
        ( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0)
        | ~ class_Lattices_Olattice(X0) )
    | ~ spl0_225 ),
    inference(avatar_component_clause,[],[f1965]) ).

fof(f2067,plain,
    spl0_250,
    inference(avatar_split_clause,[],[f715,f2065]) ).

fof(f2065,plain,
    ( spl0_250
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X4,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f715,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X4,tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mpoly__base__conv_I1_J_0) ).

fof(f2063,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f639,f2061]) ).

fof(f2061,plain,
    ( spl0_249
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f639,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(f2059,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f638,f2057]) ).

fof(f2057,plain,
    ( spl0_248
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f638,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f2055,plain,
    ( spl0_247
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1892,f1877,f1308,f2053]) ).

fof(f2053,plain,
    ( spl0_247
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f1308,plain,
    ( spl0_78
  <=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f1877,plain,
    ( spl0_205
  <=> ! [X4,X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1892,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0
    | ~ spl0_78
    | ~ spl0_205 ),
    inference(resolution,[],[f1878,f1310]) ).

fof(f1310,plain,
    ( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f1308]) ).

fof(f1878,plain,
    ( ! [X0,X4] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X0) = X4 )
    | ~ spl0_205 ),
    inference(avatar_component_clause,[],[f1877]) ).

fof(f2051,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f637,f2049]) ).

fof(f2049,plain,
    ( spl0_246
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f637,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f2047,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f564,f2045]) ).

fof(f2045,plain,
    ( spl0_245
  <=> ! [X5,X4,X0] :
        ( ~ class_HOL_Oeq(X0)
        | X4 = X5
        | ~ c_HOL_Oeq__class_Oeq(X4,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f564,axiom,
    ! [X0,X4,X5] :
      ( ~ class_HOL_Oeq(X0)
      | X4 = X5
      | ~ c_HOL_Oeq__class_Oeq(X4,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equals_0) ).

fof(f2043,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f534,f2041]) ).

fof(f2041,plain,
    ( spl0_244
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f534,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f2039,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f533,f2037]) ).

fof(f2037,plain,
    ( spl0_243
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f533,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f2035,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f532,f2033]) ).

fof(f2033,plain,
    ( spl0_242
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f532,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f2031,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f524,f2029]) ).

fof(f2029,plain,
    ( spl0_241
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f524,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pprt__0_0) ).

fof(f2027,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f521,f2025]) ).

fof(f2025,plain,
    ( spl0_240
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f521,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).

fof(f2023,plain,
    spl0_239,
    inference(avatar_split_clause,[],[f520,f2021]) ).

fof(f2021,plain,
    ( spl0_239
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f520,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

fof(f2019,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f518,f2017]) ).

fof(f2017,plain,
    ( spl0_238
  <=> ! [X4,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f518,axiom,
    ! [X0,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

fof(f2015,plain,
    spl0_237,
    inference(avatar_split_clause,[],[f511,f2013]) ).

fof(f2013,plain,
    ( spl0_237
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f511,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__0_0) ).

fof(f2011,plain,
    ( spl0_236
    | ~ spl0_26
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1891,f1877,f1048,f2009]) ).

fof(f2009,plain,
    ( spl0_236
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f1048,plain,
    ( spl0_26
  <=> class_Lattices_Olower__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1891,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
    | ~ spl0_26
    | ~ spl0_205 ),
    inference(resolution,[],[f1878,f1050]) ).

fof(f1050,plain,
    ( class_Lattices_Olower__semilattice(tc_nat)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f1048]) ).

fof(f2007,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f495,f2005]) ).

fof(f2005,plain,
    ( spl0_235
  <=> ! [X0] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f495,axiom,
    ! [X0] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).

fof(f2003,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f494,f2001]) ).

fof(f2001,plain,
    ( spl0_234
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osgn__if(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f494,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osgn__if(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).

fof(f1999,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f493,f1997]) ).

fof(f1997,plain,
    ( spl0_233
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f493,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).

fof(f1995,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f491,f1993]) ).

fof(f1993,plain,
    ( spl0_232
  <=> ! [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_232])]) ).

fof(f491,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).

fof(f1991,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f490,f1989]) ).

fof(f1989,plain,
    ( spl0_231
  <=> ! [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_231])]) ).

fof(f490,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

fof(f1987,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f478,f1985]) ).

fof(f1985,plain,
    ( spl0_230
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f478,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).

fof(f1983,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f418,f1981]) ).

fof(f1981,plain,
    ( spl0_229
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f418,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nprt__le__zero_0) ).

fof(f1979,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f359,f1977]) ).

fof(f1977,plain,
    ( spl0_228
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f359,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1975,plain,
    spl0_227,
    inference(avatar_split_clause,[],[f358,f1973]) ).

fof(f1973,plain,
    ( spl0_227
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f358,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1971,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f356,f1969]) ).

fof(f1969,plain,
    ( spl0_226
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f356,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X5,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1967,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f355,f1965]) ).

fof(f355,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X5,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1963,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f334,f1961]) ).

fof(f1961,plain,
    ( spl0_224
  <=> ! [X0] :
        ( ~ class_RealVector_Oreal__normed__algebra__1(X0)
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f334,axiom,
    ! [X0] :
      ( ~ class_RealVector_Oreal__normed__algebra__1(X0)
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__one_0) ).

fof(f1959,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f256,f1957]) ).

fof(f1957,plain,
    ( spl0_223
  <=> ! [X2,X0,X27] :
        ( ~ class_Ring__and__Field_Odvd(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f256,axiom,
    ! [X2,X0,X27] :
      ( ~ class_Ring__and__Field_Odvd(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X27,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvdI_0) ).

fof(f1955,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f255,f1953]) ).

fof(f1953,plain,
    ( spl0_222
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f255,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

fof(f1951,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f254,f1949]) ).

fof(f1949,plain,
    ( spl0_221
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f254,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

fof(f1947,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f253,f1945]) ).

fof(f1945,plain,
    ( spl0_220
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f253,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

fof(f1943,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f252,f1941]) ).

fof(f1941,plain,
    ( spl0_219
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f252,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f1939,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f250,f1937]) ).

fof(f1937,plain,
    ( spl0_218
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f250,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f1935,plain,
    spl0_217,
    inference(avatar_split_clause,[],[f249,f1933]) ).

fof(f249,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f1931,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f248,f1929]) ).

fof(f248,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f1927,plain,
    ( spl0_215
    | ~ spl0_77
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1885,f1853,f1303,f1925]) ).

fof(f1925,plain,
    ( spl0_215
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f1303,plain,
    ( spl0_77
  <=> class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1853,plain,
    ( spl0_199
  <=> ! [X4,X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X0) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f1885,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0
    | ~ spl0_77
    | ~ spl0_199 ),
    inference(resolution,[],[f1854,f1305]) ).

fof(f1305,plain,
    ( class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1303]) ).

fof(f1854,plain,
    ( ! [X0,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X0) = X4 )
    | ~ spl0_199 ),
    inference(avatar_component_clause,[],[f1853]) ).

fof(f1923,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f212,f1921]) ).

fof(f212,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X3,X0) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__1__left_0) ).

fof(f1919,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f211,f1917]) ).

fof(f1917,plain,
    ( spl0_213
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f211,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__pprt_0) ).

fof(f1915,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f189,f1913]) ).

fof(f1913,plain,
    ( spl0_212
  <=> ! [X4,X0] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | c_HOL_Oeq__class_Oeq(X4,X4,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f189,axiom,
    ! [X0,X4] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | c_HOL_Oeq__class_Oeq(X4,X4,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__poly__def_1) ).

fof(f1911,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f48,f1909]) ).

fof(f1909,plain,
    ( spl0_211
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f48,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f1907,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f47,f1905]) ).

fof(f1905,plain,
    ( spl0_210
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olattice(X0)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f47,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olattice(X0)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f1903,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f46,f1901]) ).

fof(f1901,plain,
    ( spl0_209
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f46,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f1899,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f45,f1897]) ).

fof(f1897,plain,
    ( spl0_208
  <=> ! [X5,X4,X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f45,axiom,
    ! [X0,X4,X5] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X5,X0),X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f1890,plain,
    ( spl0_207
    | ~ spl0_25
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1884,f1853,f1043,f1888]) ).

fof(f1043,plain,
    ( spl0_25
  <=> class_Lattices_Oupper__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1884,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
    | ~ spl0_25
    | ~ spl0_199 ),
    inference(resolution,[],[f1854,f1045]) ).

fof(f1045,plain,
    ( class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f1043]) ).

fof(f1883,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f632,f1881]) ).

fof(f1881,plain,
    ( spl0_206
  <=> ! [X6,X19] :
        ( c_lessequals(X6,X19,tc_RealDef_Oreal)
        | c_lessequals(X19,X6,tc_RealDef_Oreal) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f632,axiom,
    ! [X6,X19] :
      ( c_lessequals(X6,X19,tc_RealDef_Oreal)
      | c_lessequals(X19,X6,tc_RealDef_Oreal) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).

fof(f1879,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f591,f1877]) ).

fof(f591,axiom,
    ! [X0,X4] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X0) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1875,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f568,f1873]) ).

fof(f1873,plain,
    ( spl0_204
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f568,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

fof(f1871,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f550,f1869]) ).

fof(f1869,plain,
    ( spl0_203
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f550,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

fof(f1867,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f537,f1865]) ).

fof(f1865,plain,
    ( spl0_202
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f537,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

fof(f1863,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f433,f1861]) ).

fof(f1861,plain,
    ( spl0_201
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f433,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

fof(f1859,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f422,f1857]) ).

fof(f1857,plain,
    ( spl0_200
  <=> ! [X40,X33] :
        ( X33 = X40
        | c_Suc(X33) != c_Suc(X40) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f422,axiom,
    ! [X40,X33] :
      ( X33 = X40
      | c_Suc(X33) != c_Suc(X40) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

fof(f1855,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f278,f1853]) ).

fof(f278,axiom,
    ! [X0,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X0) = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1851,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f916,f1849]) ).

fof(f1849,plain,
    ( spl0_198
  <=> ! [X45] :
        ( ~ class_HOL_Ozero(X45)
        | ~ class_HOL_Oeq(X45)
        | class_HOL_Oeq(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f916,axiom,
    ! [X45] :
      ( ~ class_HOL_Ozero(X45)
      | ~ class_HOL_Oeq(X45)
      | class_HOL_Oeq(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Oeq) ).

fof(f1847,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f669,f1845]) ).

fof(f1845,plain,
    ( spl0_197
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f669,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__pos__poly__0_0) ).

fof(f1843,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f513,f1841]) ).

fof(f1841,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

fof(f513,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/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

fof(f1839,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f507,f1837]) ).

fof(f1837,plain,
    ( spl0_195
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f507,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

fof(f1835,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f49,f1833]) ).

fof(f1833,plain,
    ( spl0_194
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f49,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__dvd_0) ).

fof(f1831,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f599,f1829]) ).

fof(f1829,plain,
    ( spl0_193
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f599,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f1827,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f598,f1825]) ).

fof(f1825,plain,
    ( spl0_192
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f598,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Opreorder(X0)
      | c_lessequals(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f1823,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f544,f1821]) ).

fof(f1821,plain,
    ( spl0_191
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f544,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1819,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f543,f1817]) ).

fof(f1817,plain,
    ( spl0_190
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f543,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1815,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f542,f1813]) ).

fof(f1813,plain,
    ( spl0_189
  <=> ! [X4,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f542,axiom,
    ! [X0,X4] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1811,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f190,f1809]) ).

fof(f1809,plain,
    ( spl0_188
  <=> ! [X4,X0] :
        ( ~ class_HOL_Oeq(X0)
        | c_HOL_Oeq__class_Oeq(X4,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f190,axiom,
    ! [X0,X4] :
      ( ~ class_HOL_Oeq(X0)
      | c_HOL_Oeq__class_Oeq(X4,X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).

fof(f1807,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f68,f1805]) ).

fof(f1805,plain,
    ( spl0_187
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f68,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

fof(f1803,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f915,f1801]) ).

fof(f1801,plain,
    ( spl0_186
  <=> ! [X45] :
        ( ~ class_HOL_Ozero(X45)
        | class_HOL_Ozero(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f915,axiom,
    ! [X45] :
      ( ~ class_HOL_Ozero(X45)
      | class_HOL_Ozero(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).

fof(f1799,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f914,f1797]) ).

fof(f1797,plain,
    ( spl0_185
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X45)
        | class_Int_Onumber__ring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f914,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X45)
      | class_Int_Onumber__ring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

fof(f1795,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f913,f1793]) ).

fof(f1793,plain,
    ( spl0_184
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Orderings_Oorder(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f913,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Orderings_Oorder(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).

fof(f1791,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f912,f1789]) ).

fof(f1789,plain,
    ( spl0_183
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Orderings_Olinorder(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f912,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Orderings_Olinorder(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).

fof(f1787,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f911,f1785]) ).

fof(f1785,plain,
    ( spl0_182
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Orderings_Opreorder(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f911,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Orderings_Opreorder(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).

fof(f1783,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f910,f1781]) ).

fof(f1781,plain,
    ( spl0_181
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
        | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f910,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).

fof(f1779,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f909,f1777]) ).

fof(f1777,plain,
    ( spl0_180
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oidom(X45)
        | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f909,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oidom(X45)
      | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).

fof(f1775,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f908,f1773]) ).

fof(f1773,plain,
    ( spl0_179
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X45)
        | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f908,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X45)
      | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).

fof(f1771,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f907,f1769]) ).

fof(f1769,plain,
    ( spl0_178
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f907,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).

fof(f1767,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f906,f1765]) ).

fof(f1765,plain,
    ( spl0_177
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Oab__group__add(X45)
        | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f906,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Oab__group__add(X45)
      | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).

fof(f1763,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f905,f1761]) ).

fof(f1761,plain,
    ( spl0_176
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
        | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f905,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
      | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).

fof(f1759,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f904,f1757]) ).

fof(f1757,plain,
    ( spl0_175
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
        | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f904,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
      | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).

fof(f1755,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f903,f1753]) ).

fof(f1753,plain,
    ( spl0_174
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
        | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f903,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).

fof(f1751,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f902,f1749]) ).

fof(f1749,plain,
    ( spl0_173
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X45)
        | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f902,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X45)
      | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).

fof(f1747,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f901,f1745]) ).

fof(f1745,plain,
    ( spl0_172
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f901,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).

fof(f1743,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f900,f1741]) ).

fof(f1741,plain,
    ( spl0_171
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
        | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f900,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
      | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).

fof(f1739,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f899,f1737]) ).

fof(f1737,plain,
    ( spl0_170
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Oab__group__add(X45)
        | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f899,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Oab__group__add(X45)
      | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).

fof(f1735,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f898,f1733]) ).

fof(f1733,plain,
    ( spl0_169
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f898,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).

fof(f1731,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f897,f1729]) ).

fof(f1729,plain,
    ( spl0_168
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X45)
        | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f897,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X45)
      | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).

fof(f1727,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f896,f1725]) ).

fof(f1725,plain,
    ( spl0_167
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f896,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).

fof(f1723,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f895,f1721]) ).

fof(f1721,plain,
    ( spl0_166
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
        | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f895,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).

fof(f1719,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f894,f1717]) ).

fof(f1717,plain,
    ( spl0_165
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
        | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f894,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
      | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).

fof(f1715,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f893,f1713]) ).

fof(f1713,plain,
    ( spl0_164
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
        | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f893,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
      | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).

fof(f1711,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f892,f1709]) ).

fof(f1709,plain,
    ( spl0_163
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f892,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).

fof(f1707,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f891,f1705]) ).

fof(f1705,plain,
    ( spl0_162
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
        | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f891,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X45)
      | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).

fof(f1703,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f890,f1701]) ).

fof(f1701,plain,
    ( spl0_161
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
        | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f890,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1699,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f889,f1697]) ).

fof(f1697,plain,
    ( spl0_160
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
        | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f889,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
      | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).

fof(f1695,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f888,f1693]) ).

fof(f1693,plain,
    ( spl0_159
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
        | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f888,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X45)
      | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

fof(f1691,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f887,f1689]) ).

fof(f1689,plain,
    ( spl0_158
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
        | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f887,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X45)
      | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1687,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f886,f1685]) ).

fof(f1685,plain,
    ( spl0_157
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f886,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).

fof(f1683,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f885,f1681]) ).

fof(f1681,plain,
    ( spl0_156
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oidom(X45)
        | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f885,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oidom(X45)
      | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).

fof(f1679,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f884,f1677]) ).

fof(f1677,plain,
    ( spl0_155
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f884,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).

fof(f1675,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f883,f1673]) ).

fof(f1673,plain,
    ( spl0_154
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f883,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).

fof(f1671,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f882,f1669]) ).

fof(f1669,plain,
    ( spl0_153
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
        | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f882,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
      | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1667,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f881,f1665]) ).

fof(f1665,plain,
    ( spl0_152
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f881,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).

fof(f1663,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f880,f1661]) ).

fof(f1661,plain,
    ( spl0_151
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f880,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).

fof(f1659,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f879,f1657]) ).

fof(f1657,plain,
    ( spl0_150
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f879,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).

fof(f1655,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f878,f1653]) ).

fof(f1653,plain,
    ( spl0_149
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f878,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1651,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f877,f1649]) ).

fof(f1649,plain,
    ( spl0_148
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oidom(X45)
        | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f877,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oidom(X45)
      | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1647,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f876,f1645]) ).

fof(f1645,plain,
    ( spl0_147
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f876,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f1643,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f875,f1641]) ).

fof(f1641,plain,
    ( spl0_146
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f875,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f1639,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f874,f1637]) ).

fof(f1637,plain,
    ( spl0_145
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f874,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).

fof(f1635,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f873,f1633]) ).

fof(f1633,plain,
    ( spl0_144
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f873,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f1631,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f872,f1629]) ).

fof(f1629,plain,
    ( spl0_143
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f872,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f1627,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f871,f1625]) ).

fof(f1625,plain,
    ( spl0_142
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f871,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f1623,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f870,f1621]) ).

fof(f1621,plain,
    ( spl0_141
  <=> ! [X45] :
        ( ~ class_Ring__and__Field_Oordered__idom(X45)
        | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f870,axiom,
    ! [X45] :
      ( ~ class_Ring__and__Field_Oordered__idom(X45)
      | class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f1619,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f737,f1617]) ).

fof(f1617,plain,
    ( spl0_140
  <=> ! [X45] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
        | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X45)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f737,axiom,
    ! [X45] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X45)
      | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X45)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f1615,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f562,f1613]) ).

fof(f1613,plain,
    ( spl0_139
  <=> ! [X33] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X33) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f562,axiom,
    ! [X33] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

fof(f1611,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f471,f1609]) ).

fof(f1609,plain,
    ( spl0_138
  <=> ! [X4,X0] : c_Fun_Oid(X4,X0) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f471,axiom,
    ! [X0,X4] : c_Fun_Oid(X4,X0) = X4,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).

fof(f1607,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f741,f1605]) ).

fof(f1605,plain,
    ( spl0_137
  <=> ! [X45,X46] : class_HOL_Oeq(tc_prod(X46,X45)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f741,axiom,
    ! [X46,X45] : class_HOL_Oeq(tc_prod(X46,X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod__HOL_Oeq) ).

fof(f1603,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f601,f1601]) ).

fof(f1601,plain,
    ( spl0_136
  <=> ! [X19] : c_lessequals(X19,X19,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f601,axiom,
    ! [X19] : c_lessequals(X19,X19,tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

fof(f1599,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f21,f1597]) ).

fof(f1597,plain,
    ( spl0_135
  <=> ! [X10] : c_Suc(X10) != X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f21,axiom,
    ! [X10] : c_Suc(X10) != X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

fof(f1595,plain,
    ( ~ spl0_134
    | ~ spl0_133 ),
    inference(avatar_split_clause,[],[f1589,f1582,f1592]) ).

fof(f1589,plain,
    ( v_c != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
    | ~ spl0_133 ),
    inference(trivial_inequality_removal,[],[f1588]) ).

fof(f1588,plain,
    ( v_c != v_c
    | v_c != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
    | ~ spl0_133 ),
    inference(forward_demodulation,[],[f918,f1584]) ).

fof(f1584,plain,
    ( v_c = v_y
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1582]) ).

fof(f918,plain,
    ( v_c != v_y
    | v_c != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
    inference(inner_rewriting,[],[f735]) ).

fof(f735,axiom,
    ( v_c != v_y
    | v_y != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f1587,plain,
    ( ~ spl0_133
    | spl0_132 ),
    inference(avatar_split_clause,[],[f1586,f1578,f1582]) ).

fof(f1586,plain,
    ( v_c != v_y
    | spl0_132 ),
    inference(forward_demodulation,[],[f1579,f734]) ).

fof(f1579,plain,
    ( v_y != c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
    | spl0_132 ),
    inference(avatar_component_clause,[],[f1578]) ).

fof(f1585,plain,
    ( spl0_132
    | spl0_133 ),
    inference(avatar_split_clause,[],[f736,f1582,f1578]) ).

fof(f736,axiom,
    ( v_c = v_y
    | v_y = c_Polynomial_Opoly(c_Polynomial_OpCons(v_c,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1576,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f869,f1573]) ).

fof(f1573,plain,
    ( spl0_131
  <=> class_HOL_Oeq(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f869,axiom,
    class_HOL_Oeq(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Oeq) ).

fof(f1571,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f868,f1568]) ).

fof(f1568,plain,
    ( spl0_130
  <=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f868,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

fof(f1566,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f867,f1563]) ).

fof(f1563,plain,
    ( spl0_129
  <=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f867,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(f1561,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f866,f1558]) ).

fof(f1558,plain,
    ( spl0_128
  <=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f866,axiom,
    class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).

fof(f1556,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f865,f1553]) ).

fof(f1553,plain,
    ( spl0_127
  <=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f865,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

fof(f1551,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f864,f1548]) ).

fof(f1548,plain,
    ( spl0_126
  <=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f864,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

fof(f1546,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f863,f1543]) ).

fof(f1543,plain,
    ( spl0_125
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f863,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f1541,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f862,f1538]) ).

fof(f1538,plain,
    ( spl0_124
  <=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f862,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

fof(f1536,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f861,f1533]) ).

fof(f1533,plain,
    ( spl0_123
  <=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f861,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

fof(f1531,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f860,f1528]) ).

fof(f1528,plain,
    ( spl0_122
  <=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f860,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

fof(f1526,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f859,f1523]) ).

fof(f859,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

fof(f1521,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f858,f1518]) ).

fof(f1518,plain,
    ( spl0_120
  <=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f858,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).

fof(f1516,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f857,f1513]) ).

fof(f1513,plain,
    ( spl0_119
  <=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f857,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

fof(f1511,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f856,f1508]) ).

fof(f1508,plain,
    ( spl0_118
  <=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f856,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

fof(f1506,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f855,f1503]) ).

fof(f1503,plain,
    ( spl0_117
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f855,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

fof(f1501,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f854,f1498]) ).

fof(f1498,plain,
    ( spl0_116
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f854,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

fof(f1496,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f853,f1493]) ).

fof(f1493,plain,
    ( spl0_115
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f853,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

fof(f1491,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f852,f1488]) ).

fof(f1488,plain,
    ( spl0_114
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f852,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

fof(f1486,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f851,f1483]) ).

fof(f1483,plain,
    ( spl0_113
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f851,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

fof(f1481,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f850,f1478]) ).

fof(f1478,plain,
    ( spl0_112
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f850,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1476,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f849,f1473]) ).

fof(f1473,plain,
    ( spl0_111
  <=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f849,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f1471,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f848,f1468]) ).

fof(f1468,plain,
    ( spl0_110
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f848,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

fof(f1466,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f847,f1463]) ).

fof(f1463,plain,
    ( spl0_109
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f847,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f1461,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f846,f1458]) ).

fof(f1458,plain,
    ( spl0_108
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f846,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

fof(f1456,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f845,f1453]) ).

fof(f845,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1451,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f844,f1448]) ).

fof(f1448,plain,
    ( spl0_106
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f844,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

fof(f1446,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f843,f1443]) ).

fof(f1443,plain,
    ( spl0_105
  <=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f843,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(f1441,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f842,f1438]) ).

fof(f1438,plain,
    ( spl0_104
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f842,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1436,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f841,f1433]) ).

fof(f1433,plain,
    ( spl0_103
  <=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f841,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

fof(f1431,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f840,f1428]) ).

fof(f1428,plain,
    ( spl0_102
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f840,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1426,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f839,f1423]) ).

fof(f1423,plain,
    ( spl0_101
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f839,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1421,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f838,f1418]) ).

fof(f1418,plain,
    ( spl0_100
  <=> class_HOL_Oeq(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f838,axiom,
    class_HOL_Oeq(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oeq) ).

fof(f1416,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f837,f1413]) ).

fof(f1413,plain,
    ( spl0_99
  <=> class_HOL_Ozero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f837,axiom,
    class_HOL_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).

fof(f1411,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f836,f1408]) ).

fof(f1408,plain,
    ( spl0_98
  <=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f836,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

fof(f1406,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f835,f1403]) ).

fof(f1403,plain,
    ( spl0_97
  <=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f835,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

fof(f1401,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f834,f1398]) ).

fof(f1398,plain,
    ( spl0_96
  <=> class_Lattices_Olattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f834,axiom,
    class_Lattices_Olattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).

fof(f1396,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f833,f1393]) ).

fof(f1393,plain,
    ( spl0_95
  <=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f833,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

fof(f1391,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f832,f1388]) ).

fof(f1388,plain,
    ( spl0_94
  <=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f832,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

fof(f1386,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f831,f1383]) ).

fof(f1383,plain,
    ( spl0_93
  <=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f831,axiom,
    class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).

fof(f1381,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f830,f1378]) ).

fof(f1378,plain,
    ( spl0_92
  <=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f830,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

fof(f1376,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f829,f1373]) ).

fof(f1373,plain,
    ( spl0_91
  <=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f829,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

fof(f1371,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f828,f1368]) ).

fof(f1368,plain,
    ( spl0_90
  <=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f828,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

fof(f1366,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f827,f1363]) ).

fof(f1363,plain,
    ( spl0_89
  <=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f827,axiom,
    class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).

fof(f1361,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f826,f1358]) ).

fof(f1358,plain,
    ( spl0_88
  <=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f826,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

fof(f1356,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f825,f1353]) ).

fof(f1353,plain,
    ( spl0_87
  <=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f825,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

fof(f1351,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f824,f1348]) ).

fof(f1348,plain,
    ( spl0_86
  <=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f824,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

fof(f1346,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f823,f1343]) ).

fof(f1343,plain,
    ( spl0_85
  <=> class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f823,axiom,
    class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).

fof(f1341,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f822,f1338]) ).

fof(f822,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

fof(f1336,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f821,f1333]) ).

fof(f1333,plain,
    ( spl0_83
  <=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f821,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).

fof(f1331,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f820,f1328]) ).

fof(f1328,plain,
    ( spl0_82
  <=> class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f820,axiom,
    class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).

fof(f1326,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f819,f1323]) ).

fof(f1323,plain,
    ( spl0_81
  <=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f819,axiom,
    class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).

fof(f1321,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f818,f1318]) ).

fof(f1318,plain,
    ( spl0_80
  <=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f818,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

fof(f1316,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f817,f1313]) ).

fof(f1313,plain,
    ( spl0_79
  <=> class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f817,axiom,
    class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).

fof(f1311,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f816,f1308]) ).

fof(f816,axiom,
    class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).

fof(f1306,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f815,f1303]) ).

fof(f815,axiom,
    class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).

fof(f1301,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f814,f1298]) ).

fof(f1298,plain,
    ( spl0_76
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f814,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).

fof(f1296,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f813,f1293]) ).

fof(f1293,plain,
    ( spl0_75
  <=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f813,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).

fof(f1291,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f812,f1288]) ).

fof(f1288,plain,
    ( spl0_74
  <=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f812,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).

fof(f1286,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f811,f1283]) ).

fof(f1283,plain,
    ( spl0_73
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f811,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

fof(f1281,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f810,f1278]) ).

fof(f1278,plain,
    ( spl0_72
  <=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f810,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).

fof(f1276,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f809,f1273]) ).

fof(f1273,plain,
    ( spl0_71
  <=> class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f809,axiom,
    class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).

fof(f1271,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f808,f1268]) ).

fof(f1268,plain,
    ( spl0_70
  <=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f808,axiom,
    class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).

fof(f1266,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f807,f1263]) ).

fof(f1263,plain,
    ( spl0_69
  <=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f807,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

fof(f1261,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f806,f1258]) ).

fof(f1258,plain,
    ( spl0_68
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f806,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1256,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f805,f1253]) ).

fof(f1253,plain,
    ( spl0_67
  <=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f805,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(f1251,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f804,f1248]) ).

fof(f1248,plain,
    ( spl0_66
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f804,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

fof(f1246,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f803,f1243]) ).

fof(f1243,plain,
    ( spl0_65
  <=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f803,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(f1241,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f802,f1238]) ).

fof(f1238,plain,
    ( spl0_64
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f802,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).

fof(f1236,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f801,f1233]) ).

fof(f801,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1231,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f800,f1228]) ).

fof(f1228,plain,
    ( spl0_62
  <=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f800,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).

fof(f1226,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f799,f1223]) ).

fof(f1223,plain,
    ( spl0_61
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f799,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).

fof(f1221,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f798,f1218]) ).

fof(f1218,plain,
    ( spl0_60
  <=> class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f798,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).

fof(f1216,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f797,f1213]) ).

fof(f1213,plain,
    ( spl0_59
  <=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f797,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

fof(f1211,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f796,f1208]) ).

fof(f1208,plain,
    ( spl0_58
  <=> class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f796,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).

fof(f1206,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f795,f1203]) ).

fof(f1203,plain,
    ( spl0_57
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f795,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1201,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f794,f1198]) ).

fof(f1198,plain,
    ( spl0_56
  <=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f794,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).

fof(f1196,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f793,f1193]) ).

fof(f1193,plain,
    ( spl0_55
  <=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f793,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).

fof(f1191,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f792,f1188]) ).

fof(f1188,plain,
    ( spl0_54
  <=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f792,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).

fof(f1186,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f791,f1183]) ).

fof(f1183,plain,
    ( spl0_53
  <=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f791,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

fof(f1181,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f790,f1178]) ).

fof(f1178,plain,
    ( spl0_52
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f790,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).

fof(f1176,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f789,f1173]) ).

fof(f1173,plain,
    ( spl0_51
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f789,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1171,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f788,f1168]) ).

fof(f1168,plain,
    ( spl0_50
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f788,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1166,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f787,f1163]) ).

fof(f1163,plain,
    ( spl0_49
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f787,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f1161,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f786,f1158]) ).

fof(f1158,plain,
    ( spl0_48
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f786,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f1156,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f785,f1153]) ).

fof(f1153,plain,
    ( spl0_47
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f785,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).

fof(f1151,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f784,f1148]) ).

fof(f1148,plain,
    ( spl0_46
  <=> class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f784,axiom,
    class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) ).

fof(f1146,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f783,f1143]) ).

fof(f1143,plain,
    ( spl0_45
  <=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f783,axiom,
    class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).

fof(f1141,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f782,f1138]) ).

fof(f1138,plain,
    ( spl0_44
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f782,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f1136,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f781,f1133]) ).

fof(f1133,plain,
    ( spl0_43
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f781,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f1131,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f780,f1128]) ).

fof(f1128,plain,
    ( spl0_42
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f780,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f1126,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f779,f1123]) ).

fof(f1123,plain,
    ( spl0_41
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f779,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f1121,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f778,f1118]) ).

fof(f1118,plain,
    ( spl0_40
  <=> class_HOL_Oeq(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f778,axiom,
    class_HOL_Oeq(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oeq) ).

fof(f1116,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f777,f1113]) ).

fof(f1113,plain,
    ( spl0_39
  <=> class_HOL_Ozero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f777,axiom,
    class_HOL_Ozero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).

fof(f1111,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f776,f1108]) ).

fof(f1108,plain,
    ( spl0_38
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f776,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f1106,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f775,f1103]) ).

fof(f775,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f1101,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f774,f1098]) ).

fof(f1098,plain,
    ( spl0_36
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f774,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f1096,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f773,f1093]) ).

fof(f1093,plain,
    ( spl0_35
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f773,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f1091,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f772,f1088]) ).

fof(f1088,plain,
    ( spl0_34
  <=> class_Ring__and__Field_Odvd(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f772,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

fof(f1086,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f771,f1083]) ).

fof(f1083,plain,
    ( spl0_33
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f771,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f1081,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f770,f1078]) ).

fof(f1078,plain,
    ( spl0_32
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f770,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f1076,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f769,f1073]) ).

fof(f1073,plain,
    ( spl0_31
  <=> class_Lattices_Odistrib__lattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f769,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

fof(f1071,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f768,f1068]) ).

fof(f768,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f1066,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f767,f1063]) ).

fof(f1063,plain,
    ( spl0_29
  <=> class_Ring__and__Field_Omult__mono(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f767,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(f1061,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f766,f1058]) ).

fof(f1058,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f766,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f1056,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f765,f1053]) ).

fof(f1053,plain,
    ( spl0_27
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f765,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(f1051,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f764,f1048]) ).

fof(f764,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

fof(f1046,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f763,f1043]) ).

fof(f763,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

fof(f1041,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f762,f1038]) ).

fof(f1038,plain,
    ( spl0_24
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f762,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

fof(f1036,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f761,f1033]) ).

fof(f1033,plain,
    ( spl0_23
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f761,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f1031,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f760,f1028]) ).

fof(f1028,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f760,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f1026,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f759,f1023]) ).

fof(f1023,plain,
    ( spl0_21
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f759,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f1021,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f758,f1018]) ).

fof(f1018,plain,
    ( spl0_20
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f758,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1016,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f757,f1013]) ).

fof(f1013,plain,
    ( spl0_19
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f757,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f1011,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f756,f1008]) ).

fof(f1008,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f756,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).

fof(f1006,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f755,f1003]) ).

fof(f755,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1001,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f754,f998]) ).

fof(f998,plain,
    ( spl0_16
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f754,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f996,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f753,f993]) ).

fof(f993,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f753,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(f991,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f752,f988]) ).

fof(f988,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f752,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(f986,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f751,f983]) ).

fof(f983,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f751,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(f981,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f750,f978]) ).

fof(f978,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f750,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f976,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f749,f973]) ).

fof(f973,plain,
    ( spl0_11
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f749,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f971,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f748,f968]) ).

fof(f968,plain,
    ( spl0_10
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f748,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f966,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f747,f963]) ).

fof(f963,plain,
    ( spl0_9
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f747,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f961,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f746,f958]) ).

fof(f958,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f746,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(f956,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f745,f953]) ).

fof(f953,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f745,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f951,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f744,f948]) ).

fof(f948,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f744,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f946,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f743,f943]) ).

fof(f943,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f743,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f941,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f742,f938]) ).

fof(f938,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f742,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f936,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f740,f933]) ).

fof(f933,plain,
    ( spl0_3
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f740,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f931,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f739,f928]) ).

fof(f928,plain,
    ( spl0_2
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f739,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f926,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f738,f923]) ).

fof(f923,plain,
    ( spl0_1
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f738,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : ALG439-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n022.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Fri May  3 19:54:52 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  % (31112)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.37  % (31115)WARNING: value z3 for option sas not known
% 0.16/0.37  % (31117)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)
% 0.16/0.37  % (31114)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.37  % (31118)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)
% 0.16/0.37  % (31113)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.37  % (31119)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.16/0.37  % (31116)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.37  % (31115)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)
% 0.16/0.42  % (31117)First to succeed.
% 0.16/0.43  % (31115)Also succeeded, but the first one will report.
% 0.16/0.43  % (31117)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31112"
% 0.16/0.43  % (31117)Refutation found. Thanks to Tanya!
% 0.16/0.43  % SZS status Unsatisfiable for theBenchmark
% 0.16/0.43  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.44  % (31117)------------------------------
% 0.16/0.44  % (31117)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.44  % (31117)Termination reason: Refutation
% 0.16/0.44  
% 0.16/0.44  % (31117)Memory used [KB]: 2430
% 0.16/0.44  % (31117)Time elapsed: 0.060 s
% 0.16/0.44  % (31117)Instructions burned: 108 (million)
% 0.16/0.44  % (31112)Success in time 0.11 s
%------------------------------------------------------------------------------