TSTP Solution File: SWV689-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n024.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Sep  2 13:57:38 EDT 2023

% Result   : Unsatisfiable 0.28s 0.58s
% Output   : Refutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  399
% Syntax   : Number of formulae    :  639 ( 271 unt;   0 def)
%            Number of atoms       : 1204 ( 164 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  957 ( 392   ~; 359   |;   0   &)
%                                         ( 206 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :  253 ( 251 usr; 207 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :  665 (; 665   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2618,plain,
    $false,
    inference(avatar_sat_refutation,[],[f815,f820,f825,f830,f835,f840,f845,f850,f855,f860,f865,f870,f875,f880,f885,f890,f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f969,f973,f978,f982,f986,f991,f995,f999,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1067,f1071,f1075,f1079,f1083,f1087,f1091,f1095,f1099,f1103,f1118,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1174,f1196,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1250,f1254,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1286,f1290,f1294,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1386,f1390,f1448,f1524,f1582,f1614,f1618,f1622,f1626,f1630,f1634,f1638,f1645,f1649,f1653,f1657,f1661,f1665,f1669,f1673,f1677,f1681,f1690,f1694,f1698,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1870,f2027,f2045,f2049,f2053,f2057,f2061,f2065,f2069,f2073,f2077,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2110,f2114,f2118,f2122,f2126,f2130,f2134,f2138,f2142,f2146,f2150,f2154,f2158,f2162,f2167,f2171,f2175,f2179,f2183,f2187,f2241,f2616,f2617]) ).

fof(f2617,plain,
    ( ~ spl0_37
    | spl0_1
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f2537,f2181,f812,f988]) ).

fof(f988,plain,
    ( spl0_37
  <=> c_HOL_Oord__class_Oless(v_i,v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f812,plain,
    ( spl0_1
  <=> c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f2181,plain,
    ( spl0_202
  <=> ! [X9,X7,X4] :
        ( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f2537,plain,
    ( ~ c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
    | spl0_1
    | ~ spl0_202 ),
    inference(resolution,[],[f2182,f814]) ).

fof(f814,plain,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f812]) ).

fof(f2182,plain,
    ( ! [X9,X7,X4] :
        ( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f2181]) ).

fof(f2616,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f30,f2614]) ).

fof(f2614,plain,
    ( spl0_206
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f30,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__of__nonneg_0) ).

fof(f2241,plain,
    ( spl0_204
    | ~ spl0_205
    | ~ spl0_166
    | ~ spl0_169 ),
    inference(avatar_split_clause,[],[f2220,f2047,f1867,f2238,f2234]) ).

fof(f2234,plain,
    ( spl0_204
  <=> v_n = c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f2238,plain,
    ( spl0_205
  <=> c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).

fof(f1867,plain,
    ( spl0_166
  <=> c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f2047,plain,
    ( spl0_169
  <=> ! [X4,X3] :
        ( X3 = X4
        | ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f2220,plain,
    ( ~ c_lessequals(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat)
    | v_n = c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat)
    | ~ spl0_166
    | ~ spl0_169 ),
    inference(resolution,[],[f2048,f1869]) ).

fof(f1869,plain,
    ( c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1867]) ).

fof(f2048,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat)
        | X3 = X4 )
    | ~ spl0_169 ),
    inference(avatar_component_clause,[],[f2047]) ).

fof(f2187,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f758,f2185]) ).

fof(f2185,plain,
    ( spl0_203
  <=> ! [X4,X3] :
        ( X3 = X4
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f758,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__neq__iff_0) ).

fof(f2183,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f750,f2181]) ).

fof(f750,axiom,
    ! [X9,X7,X4] :
      ( ~ c_HOL_Oord__class_Oless(X7,X9,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X4,tc_nat),X9,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__imp__diff__less_0) ).

fof(f2179,plain,
    spl0_201,
    inference(avatar_split_clause,[],[f697,f2177]) ).

fof(f2177,plain,
    ( spl0_201
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f697,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__Suc__Suc_0) ).

fof(f2175,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f687,f2173]) ).

fof(f2173,plain,
    ( spl0_200
  <=> ! [X9,X8,X7] :
        ( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).

fof(f687,axiom,
    ! [X8,X9,X7] :
      ( c_HOL_Oord__class_Oless(X8,X9,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X9,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__lessD1_0) ).

fof(f2171,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f686,f2169]) ).

fof(f2169,plain,
    ( spl0_199
  <=> ! [X6,X5,X15] :
        ( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).

fof(f686,axiom,
    ! [X6,X15,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X15,tc_nat)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I2_J_0) ).

fof(f2167,plain,
    ( spl0_198
    | ~ spl0_37
    | ~ spl0_159 ),
    inference(avatar_split_clause,[],[f1962,f1732,f988,f2164]) ).

fof(f2164,plain,
    ( spl0_198
  <=> v_i = c_Divides_Odiv__class_Omod(v_i,v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).

fof(f1732,plain,
    ( spl0_159
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f1962,plain,
    ( v_i = c_Divides_Odiv__class_Omod(v_i,v_n,tc_nat)
    | ~ spl0_37
    | ~ spl0_159 ),
    inference(resolution,[],[f1733,f990]) ).

fof(f990,plain,
    ( c_HOL_Oord__class_Oless(v_i,v_n,tc_nat)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f988]) ).

fof(f1733,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 )
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1732]) ).

fof(f2162,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f685,f2160]) ).

fof(f2160,plain,
    ( spl0_197
  <=> ! [X6,X5,X15] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).

fof(f685,axiom,
    ! [X6,X15,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
      | c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I1_J_0) ).

fof(f2158,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f675,f2156]) ).

fof(f2156,plain,
    ( spl0_196
  <=> ! [X4,X3] :
        ( X3 = X4
        | ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).

fof(f675,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__eq__less__or__eq_0) ).

fof(f2154,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f587,f2152]) ).

fof(f2152,plain,
    ( spl0_195
  <=> ! [X4,X9] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).

fof(f587,axiom,
    ! [X9,X4] :
      ( c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__reduce_0) ).

fof(f2150,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f586,f2148]) ).

fof(f2148,plain,
    ( spl0_194
  <=> ! [X4,X9] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
        | c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f586,axiom,
    ! [X9,X4] :
      ( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X4,tc_nat)
      | c_Ring__and__Field_Odvd__class_Odvd(X9,c_HOL_Oplus__class_Oplus(X4,X9,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__reduce_1) ).

fof(f2146,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f554,f2144]) ).

fof(f2144,plain,
    ( spl0_193
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X1,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f554,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,X0),X1,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__diff__cancel_0) ).

fof(f2142,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f545,f2140]) ).

fof(f2140,plain,
    ( spl0_192
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X0),X1,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).

fof(f545,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X1,X0),X1,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__cancel_0) ).

fof(f2138,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f544,f2136]) ).

fof(f2136,plain,
    ( spl0_191
  <=> ! [X5,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f544,axiom,
    ! [X0,X5] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__ringb_Osubr0__iff_1) ).

fof(f2134,plain,
    spl0_190,
    inference(avatar_split_clause,[],[f472,f2132]) ).

fof(f2132,plain,
    ( spl0_190
  <=> ! [X5,X0] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f472,axiom,
    ! [X0,X5] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f2130,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f430,f2128]) ).

fof(f2128,plain,
    ( spl0_189
  <=> ! [X2,X0,X1] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f430,axiom,
    ! [X2,X0,X1] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,X1,X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__commute_0) ).

fof(f2126,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f427,f2124]) ).

fof(f2124,plain,
    ( spl0_188
  <=> ! [X2,X0,X14] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X14,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X14,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f427,axiom,
    ! [X2,X0,X14] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X14,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X14,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(f2122,plain,
    ( spl0_187
    | ~ spl0_50
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1865,f1663,f1041,f2120]) ).

fof(f2120,plain,
    ( spl0_187
  <=> ! [X18,X19] :
        ( c_lessequals(X18,X18,X19)
        | ~ class_Orderings_Olinorder(X19) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f1041,plain,
    ( spl0_50
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1663,plain,
    ( spl0_143
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X5,X6,X0)
        | c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1865,plain,
    ( ! [X18,X19] :
        ( c_lessequals(X18,X18,X19)
        | ~ class_Orderings_Olinorder(X19) )
    | ~ spl0_50
    | ~ spl0_143 ),
    inference(duplicate_literal_removal,[],[f1858]) ).

fof(f1858,plain,
    ( ! [X18,X19] :
        ( c_lessequals(X18,X18,X19)
        | ~ class_Orderings_Olinorder(X19)
        | ~ class_Orderings_Olinorder(X19) )
    | ~ spl0_50
    | ~ spl0_143 ),
    inference(resolution,[],[f1664,f1042]) ).

fof(f1042,plain,
    ( ! [X0,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X5,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f1041]) ).

fof(f1664,plain,
    ( ! [X0,X6,X5] :
        ( c_HOL_Oord__class_Oless(X6,X5,X0)
        | c_lessequals(X5,X6,X0)
        | ~ class_Orderings_Olinorder(X0) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1663]) ).

fof(f2118,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f419,f2116]) ).

fof(f2116,plain,
    ( spl0_186
  <=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f419,axiom,
    ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__Suc__right_0) ).

fof(f2114,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f418,f2112]) ).

fof(f2112,plain,
    ( spl0_185
  <=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f418,axiom,
    ! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__Suc_0) ).

fof(f2110,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f417,f2108]) ).

fof(f2108,plain,
    ( spl0_184
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f417,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Oabs__class_Oabs(X2,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__idempotent_0) ).

fof(f2106,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f410,f2104]) ).

fof(f2104,plain,
    ( spl0_183
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).

fof(f410,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__is__0__eq_0) ).

fof(f2102,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f409,f2100]) ).

fof(f2100,plain,
    ( spl0_182
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f409,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__is__0__eq_1) ).

fof(f2098,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f379,f2096]) ).

fof(f2096,plain,
    ( spl0_181
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f379,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__0__left_0) ).

fof(f2094,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f337,f2092]) ).

fof(f2092,plain,
    ( spl0_180
  <=> ! [X3] :
        ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f337,axiom,
    ! [X3] :
      ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__1__iff__1_0) ).

fof(f2090,plain,
    spl0_179,
    inference(avatar_split_clause,[],[f307,f2088]) ).

fof(f2088,plain,
    ( spl0_179
  <=> ! [X5,X0,X6] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f307,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Orderings_Oord__class_Omin(X5,X6,X0) = c_Orderings_Oord__class_Omin(X6,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__commute_0) ).

fof(f2086,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f283,f2084]) ).

fof(f2084,plain,
    ( spl0_178
  <=> ! [X3,X7,X8] :
        ( ~ c_lessequals(X8,X7,tc_nat)
        | c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f283,axiom,
    ! [X3,X8,X7] :
      ( ~ c_lessequals(X8,X7,tc_nat)
      | c_lessequals(X8,c_HOL_Oplus__class_Oplus(X7,X3,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_trans__le__add1_0) ).

fof(f2082,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f282,f2080]) ).

fof(f2080,plain,
    ( spl0_177
  <=> ! [X4,X9,X3] :
        ( c_lessequals(X9,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f282,axiom,
    ! [X3,X9,X4] :
      ( c_lessequals(X9,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__leE_1) ).

fof(f2077,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f281,f2075]) ).

fof(f2075,plain,
    ( spl0_176
  <=> ! [X4,X9,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f281,axiom,
    ! [X3,X9,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X9,tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__leE_0) ).

fof(f2073,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f280,f2071]) ).

fof(f2071,plain,
    ( spl0_175
  <=> ! [X6,X5,X15] :
        ( ~ c_lessequals(X5,X15,tc_nat)
        | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f280,axiom,
    ! [X6,X15,X5] :
      ( ~ c_lessequals(X5,X15,tc_nat)
      | c_lessequals(X5,c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I4_J_0) ).

fof(f2069,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f257,f2067]) ).

fof(f2067,plain,
    ( spl0_174
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Nat_Osemiring__1__class_Oof__nat(X4,X0) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f257,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Nat_Osemiring__1__class_Oof__nat(X4,X0) = c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__of__nat_0) ).

fof(f2065,plain,
    spl0_173,
    inference(avatar_split_clause,[],[f162,f2063]) ).

fof(f2063,plain,
    ( spl0_173
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X2,X1,X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f162,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X2,X1,X0) = c_HOL_Otimes__class_Otimes(X1,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f2061,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f160,f2059]) ).

fof(f2059,plain,
    ( spl0_172
  <=> ! [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_172])]) ).

fof(f160,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/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_double__eq__0__iff_1) ).

fof(f2057,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f85,f2055]) ).

fof(f2055,plain,
    ( spl0_171
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f85,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__is__0_1) ).

fof(f2053,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f84,f2051]) ).

fof(f2051,plain,
    ( spl0_170
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).

fof(f84,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X3
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__is__0_0) ).

fof(f2049,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f27,f2047]) ).

fof(f27,axiom,
    ! [X3,X4] :
      ( X3 = X4
      | ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__antisym_0) ).

fof(f2045,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f26,f2043]) ).

fof(f2043,plain,
    ( spl0_168
  <=> ! [X6,X5] :
        ( X5 = X6
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f26,axiom,
    ! [X6,X5] :
      ( X5 = X6
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,tc_nat)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X5,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd_Oantisym_0) ).

fof(f2027,plain,
    ( ~ spl0_167
    | ~ spl0_76
    | ~ spl0_137 ),
    inference(avatar_split_clause,[],[f1786,f1636,f1156,f2024]) ).

fof(f2024,plain,
    ( spl0_167
  <=> c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1156,plain,
    ( spl0_76
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1636,plain,
    ( spl0_137
  <=> ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f1786,plain,
    ( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
    | ~ spl0_76
    | ~ spl0_137 ),
    inference(superposition,[],[f1637,f1157]) ).

fof(f1157,plain,
    ( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f1156]) ).

fof(f1637,plain,
    ( ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat)
    | ~ spl0_137 ),
    inference(avatar_component_clause,[],[f1636]) ).

fof(f1870,plain,
    ( ~ spl0_30
    | spl0_166
    | spl0_1
    | ~ spl0_143 ),
    inference(avatar_split_clause,[],[f1856,f1663,f812,f1867,f957]) ).

fof(f957,plain,
    ( spl0_30
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f1856,plain,
    ( c_lessequals(v_n,c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),tc_nat)
    | ~ class_Orderings_Olinorder(tc_nat)
    | spl0_1
    | ~ spl0_143 ),
    inference(resolution,[],[f1664,f814]) ).

fof(f1758,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f743,f1756]) ).

fof(f1756,plain,
    ( spl0_165
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f743,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__asym_H_0) ).

fof(f1754,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f742,f1752]) ).

fof(f1752,plain,
    ( spl0_164
  <=> ! [X5,X0,X6] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f742,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X6,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__iff__gr__or__eq_1) ).

fof(f1750,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f741,f1748]) ).

fof(f1748,plain,
    ( spl0_163
  <=> ! [X2,X0,X1] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
        | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f741,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X1,X2,X0)
      | ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_xt1_I9_J_0) ).

fof(f1746,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f740,f1744]) ).

fof(f1744,plain,
    ( spl0_162
  <=> ! [X6,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f740,axiom,
    ! [X6,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__difference__nat_2) ).

fof(f1742,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f693,f1740]) ).

fof(f1740,plain,
    ( spl0_161
  <=> ! [X4,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f693,axiom,
    ! [X4,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__0__disj_3) ).

fof(f1738,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f692,f1736]) ).

fof(f1736,plain,
    ( spl0_160
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f692,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__less__eq_0) ).

fof(f1734,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f684,f1732]) ).

fof(f684,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_Divides_Odiv__class_Omod(X3,X4,tc_nat) = X3 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__if_0) ).

fof(f1730,plain,
    ( spl0_158
    | ~ spl0_75
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1494,f1446,f1152,f1728]) ).

fof(f1728,plain,
    ( spl0_158
  <=> ! [X1] : c_lessequals(X1,c_Suc(c_Suc(X1)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1152,plain,
    ( spl0_75
  <=> ! [X6,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_lessequals(X5,X6,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f1446,plain,
    ( spl0_128
  <=> ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f1494,plain,
    ( ! [X1] : c_lessequals(X1,c_Suc(c_Suc(X1)),tc_nat)
    | ~ spl0_75
    | ~ spl0_128 ),
    inference(resolution,[],[f1447,f1153]) ).

fof(f1153,plain,
    ( ! [X6,X5] :
        ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
        | c_lessequals(X5,X6,tc_nat) )
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f1152]) ).

fof(f1447,plain,
    ( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat)
    | ~ spl0_128 ),
    inference(avatar_component_clause,[],[f1446]) ).

fof(f1726,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f663,f1724]) ).

fof(f1724,plain,
    ( spl0_157
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(X5,X6,X0)
        | c_lessequals(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f663,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X5,X6,X0)
      | c_lessequals(X6,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__linear_0) ).

fof(f1722,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f661,f1720]) ).

fof(f1720,plain,
    ( spl0_156
  <=> ! [X4,X3] :
        ( c_lessequals(X4,X3,tc_nat)
        | ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f661,axiom,
    ! [X3,X4] :
      ( c_lessequals(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__le__mono_0) ).

fof(f1718,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f660,f1716]) ).

fof(f1716,plain,
    ( spl0_155
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X4,X3,tc_nat)
        | c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f660,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X4,X3,tc_nat)
      | c_lessequals(c_Suc(X4),c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__le__mono_1) ).

fof(f1714,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f647,f1712]) ).

fof(f1712,plain,
    ( spl0_154
  <=> ! [X5,X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f647,axiom,
    ! [X19,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X19,X5,tc_nat),X19,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__eq__0__iff_1) ).

fof(f1710,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f634,f1708]) ).

fof(f1708,plain,
    ( spl0_153
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f634,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_zero__less__abs__iff_0) ).

fof(f1706,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f582,f1704]) ).

fof(f1704,plain,
    ( spl0_152
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f582,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__eq__0__iff_2) ).

fof(f1702,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f581,f1700]) ).

fof(f1700,plain,
    ( spl0_151
  <=> ! [X0,X1] :
        ( ~ 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),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f581,axiom,
    ! [X0,X1] :
      ( ~ 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),X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__eq__0__iff_1) ).

fof(f1698,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f580,f1696]) ).

fof(f1696,plain,
    ( spl0_150
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f580,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__zero__right_0) ).

fof(f1694,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f579,f1692]) ).

fof(f1692,plain,
    ( spl0_149
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f579,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__zero__left_0) ).

fof(f1690,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f578,f1688]) ).

fof(f1688,plain,
    ( spl0_148
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f578,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Omul__0_0) ).

fof(f1681,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f576,f1679]) ).

fof(f1679,plain,
    ( spl0_147
  <=> ! [X2,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f576,axiom,
    ! [X2,X0] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult_Ozero__right_0) ).

fof(f1677,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f572,f1675]) ).

fof(f1675,plain,
    ( spl0_146
  <=> ! [X6,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f572,axiom,
    ! [X0,X6] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__left_Ozero_0) ).

fof(f1673,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f571,f1671]) ).

fof(f1671,plain,
    ( spl0_145
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f571,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f1669,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f518,f1667]) ).

fof(f1667,plain,
    ( spl0_144
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ c_lessequals(X5,X6,X0)
        | ~ c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f518,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_lessequals(X5,X6,X0)
      | ~ c_HOL_Oord__class_Oless(X6,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__not__le_1) ).

fof(f1665,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f517,f1663]) ).

fof(f517,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(X5,X6,X0)
      | c_HOL_Oord__class_Oless(X6,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__not__le_0) ).

fof(f1661,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f511,f1659]) ).

fof(f1659,plain,
    ( spl0_142
  <=> ! [X5,X0,X6] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_lessequals(X6,X5,X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f511,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_lessequals(X6,X5,X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__le__not__le_1) ).

fof(f1657,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f495,f1655]) ).

fof(f1655,plain,
    ( spl0_141
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | c_lessequals(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f495,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
      | c_lessequals(X5,X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__le__less_1) ).

fof(f1653,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f494,f1651]) ).

fof(f1651,plain,
    ( spl0_140
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
        | c_lessequals(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f494,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X6,X0)
      | c_lessequals(X5,X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__imp__le_0) ).

fof(f1649,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f374,f1647]) ).

fof(f1647,plain,
    ( spl0_139
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f374,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__le__zero__iff_1) ).

fof(f1645,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f289,f1643]) ).

fof(f1643,plain,
    ( spl0_138
  <=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f289,axiom,
    ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__0_0) ).

fof(f1638,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f285,f1636]) ).

fof(f285,axiom,
    ! [X17] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_odd__nat__equiv__def2_1) ).

fof(f1634,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f266,f1632]) ).

fof(f1632,plain,
    ( spl0_136
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f266,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__square__less__zero_0) ).

fof(f1630,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f235,f1628]) ).

fof(f1628,plain,
    ( spl0_135
  <=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f235,axiom,
    ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__cube_0) ).

fof(f1626,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f203,f1624]) ).

fof(f1624,plain,
    ( spl0_134
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f203,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_zero__le__square_0) ).

fof(f1622,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f150,f1620]) ).

fof(f1620,plain,
    ( spl0_133
  <=> ! [X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f150,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc0_0) ).

fof(f1618,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f145,f1616]) ).

fof(f1616,plain,
    ( spl0_132
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f145,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__0_0) ).

fof(f1614,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f96,f1612]) ).

fof(f1612,plain,
    ( spl0_131
  <=> ! [X4,X3] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f96,axiom,
    ! [X3,X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__eq__self__zero_0) ).

fof(f1582,plain,
    ( spl0_130
    | ~ spl0_123
    | ~ spl0_128 ),
    inference(avatar_split_clause,[],[f1564,f1446,f1372,f1580]) ).

fof(f1580,plain,
    ( spl0_130
  <=> ! [X5] : ~ c_HOL_Oord__class_Oless(c_Suc(X5),X5,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1372,plain,
    ( spl0_123
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1564,plain,
    ( ! [X5] : ~ c_HOL_Oord__class_Oless(c_Suc(X5),X5,tc_nat)
    | ~ spl0_123
    | ~ spl0_128 ),
    inference(resolution,[],[f1373,f1447]) ).

fof(f1373,plain,
    ( ! [X3,X4] :
        ( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
    | ~ spl0_123 ),
    inference(avatar_component_clause,[],[f1372]) ).

fof(f1524,plain,
    ( spl0_129
    | ~ spl0_94
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1460,f1268,f1256,f1522]) ).

fof(f1522,plain,
    ( spl0_129
  <=> ! [X12] : ~ c_lessequals(c_Suc(c_Suc(X12)),X12,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f1256,plain,
    ( spl0_94
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f1268,plain,
    ( spl0_97
  <=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1460,plain,
    ( ! [X12] : ~ c_lessequals(c_Suc(c_Suc(X12)),X12,tc_nat)
    | ~ spl0_94
    | ~ spl0_97 ),
    inference(resolution,[],[f1257,f1269]) ).

fof(f1269,plain,
    ( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1268]) ).

fof(f1257,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(c_Suc(X4),X3,tc_nat)
        | ~ c_lessequals(X3,X4,tc_nat) )
    | ~ spl0_94 ),
    inference(avatar_component_clause,[],[f1256]) ).

fof(f1448,plain,
    ( spl0_128
    | ~ spl0_85
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1409,f1268,f1220,f1446]) ).

fof(f1220,plain,
    ( spl0_85
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
        | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1409,plain,
    ( ! [X10] : c_HOL_Oord__class_Oless(X10,c_Suc(c_Suc(X10)),tc_nat)
    | ~ spl0_85
    | ~ spl0_97 ),
    inference(resolution,[],[f1221,f1269]) ).

fof(f1221,plain,
    ( ! [X3,X4] :
        ( ~ c_lessequals(c_Suc(X4),X3,tc_nat)
        | c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f1220]) ).

fof(f1390,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f721,f1388]) ).

fof(f1388,plain,
    ( spl0_127
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f721,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__inverse2_0) ).

fof(f1386,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f720,f1384]) ).

fof(f1384,plain,
    ( spl0_126
  <=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f720,axiom,
    ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__add__inverse_0) ).

fof(f1382,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f678,f1380]) ).

fof(f1380,plain,
    ( spl0_125
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f678,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__SucI_0) ).

fof(f1378,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f677,f1376]) ).

fof(f1376,plain,
    ( spl0_124
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f677,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__lessD_0) ).

fof(f1374,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f672,f1372]) ).

fof(f672,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq_1) ).

fof(f1370,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f671,f1368]) ).

fof(f1368,plain,
    ( spl0_122
  <=> ! [X4,X3] :
        ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f671,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq_0) ).

fof(f1366,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f659,f1364]) ).

fof(f1364,plain,
    ( spl0_121
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f659,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__ge__zero_0) ).

fof(f1362,plain,
    spl0_120,
    inference(avatar_split_clause,[],[f620,f1360]) ).

fof(f1360,plain,
    ( spl0_120
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f620,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__leD_0) ).

fof(f1358,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f619,f1356]) ).

fof(f1356,plain,
    ( spl0_119
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_lessequals(X3,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f619,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_lessequals(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__SucI_0) ).

fof(f1354,plain,
    ( spl0_118
    | ~ spl0_30
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f1175,f1116,f957,f1352]) ).

fof(f1352,plain,
    ( spl0_118
  <=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f1116,plain,
    ( spl0_66
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1175,plain,
    ( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
    | ~ spl0_30
    | ~ spl0_66 ),
    inference(resolution,[],[f1117,f959]) ).

fof(f959,plain,
    ( class_Orderings_Olinorder(tc_nat)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f957]) ).

fof(f1117,plain,
    ( ! [X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1116]) ).

fof(f1350,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f604,f1348]) ).

fof(f1348,plain,
    ( spl0_117
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f604,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__not__less__zero_0) ).

fof(f1346,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f584,f1344]) ).

fof(f1344,plain,
    ( spl0_116
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f584,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__1_0) ).

fof(f1342,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f561,f1340]) ).

fof(f1340,plain,
    ( spl0_115
  <=> ! [X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f561,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gr0I_0) ).

fof(f1338,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f543,f1336]) ).

fof(f1336,plain,
    ( spl0_114
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f543,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X2,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__self_0) ).

fof(f1334,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f542,f1332]) ).

fof(f1332,plain,
    ( spl0_113
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f542,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__0__right_0) ).

fof(f1330,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f540,f1328]) ).

fof(f1328,plain,
    ( spl0_112
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f540,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_eq__iff__diff__eq__0_0) ).

fof(f1326,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f479,f1324]) ).

fof(f1324,plain,
    ( spl0_111
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f479,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I5_J_0) ).

fof(f1322,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f478,f1320]) ).

fof(f1320,plain,
    ( spl0_110
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f478,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f1318,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f474,f1316]) ).

fof(f1316,plain,
    ( spl0_109
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f474,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__1_0) ).

fof(f1314,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f471,f1312]) ).

fof(f1312,plain,
    ( spl0_108
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f471,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f1310,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f470,f1308]) ).

fof(f1308,plain,
    ( spl0_107
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f470,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X2,X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_add__0__left_0) ).

fof(f1306,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f469,f1304]) ).

fof(f1304,plain,
    ( spl0_106
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f469,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f1302,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f468,f1300]) ).

fof(f1300,plain,
    ( spl0_105
  <=> ! [X4,X0] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f468,axiom,
    ! [X0,X4] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__0__le__iff_0) ).

fof(f1298,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f428,f1296]) ).

fof(f1296,plain,
    ( spl0_104
  <=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f428,axiom,
    ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__add__commute_0) ).

fof(f1294,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f426,f1292]) ).

fof(f1292,plain,
    ( spl0_103
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f426,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__self_0) ).

fof(f1290,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f425,f1288]) ).

fof(f1288,plain,
    ( spl0_102
  <=> ! [X2,X0] :
        ( ~ class_Divides_Osemiring__div(X0)
        | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f425,axiom,
    ! [X2,X0] :
      ( ~ class_Divides_Osemiring__div(X0)
      | c_Divides_Odiv__class_Omod(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__by__0_0) ).

fof(f1286,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f424,f1284]) ).

fof(f1284,plain,
    ( spl0_101
  <=> ! [X6,X5] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f424,axiom,
    ! [X6,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__product__nat_1) ).

fof(f1282,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f423,f1280]) ).

fof(f1280,plain,
    ( spl0_100
  <=> ! [X6,X5] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f423,axiom,
    ! [X6,X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__product__nat_2) ).

fof(f1278,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f398,f1276]) ).

fof(f1276,plain,
    ( spl0_99
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f398,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__le_0) ).

fof(f1274,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f397,f1272]) ).

fof(f1272,plain,
    ( spl0_98
  <=> ! [X4,X3] :
        ( ~ c_lessequals(X3,X4,tc_nat)
        | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f397,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__Suc__eq__le_1) ).

fof(f1270,plain,
    ( spl0_97
    | ~ spl0_43
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f1187,f1152,f1013,f1268]) ).

fof(f1013,plain,
    ( spl0_43
  <=> ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f1187,plain,
    ( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
    | ~ spl0_43
    | ~ spl0_75 ),
    inference(resolution,[],[f1153,f1014]) ).

fof(f1014,plain,
    ( ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f1013]) ).

fof(f1266,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f380,f1264]) ).

fof(f1264,plain,
    ( spl0_96
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Osemiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f380,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Osemiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__0_0) ).

fof(f1262,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f333,f1260]) ).

fof(f1260,plain,
    ( spl0_95
  <=> ! [X0,X3] :
        ( ~ class_Ring__and__Field_Oordered__semidom(X0)
        | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f333,axiom,
    ! [X3,X0] :
      ( ~ class_Ring__and__Field_Oordered__semidom(X0)
      | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_of__nat__less__0__iff_0) ).

fof(f1258,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f319,f1256]) ).

fof(f319,axiom,
    ! [X3,X4] :
      ( ~ c_lessequals(X3,X4,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq__eq_1) ).

fof(f1254,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f318,f1252]) ).

fof(f1252,plain,
    ( spl0_93
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_lessequals(c_Suc(X4),X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f318,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(c_Suc(X4),X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less__eq__eq_0) ).

fof(f1250,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f164,f1248]) ).

fof(f1248,plain,
    ( spl0_92
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f164,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__eq__0_1) ).

fof(f1246,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f161,f1244]) ).

fof(f1244,plain,
    ( spl0_91
  <=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f161,axiom,
    ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__mult__commute_0) ).

fof(f1242,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f141,f1240]) ).

fof(f1240,plain,
    ( spl0_90
  <=> ! [X9,X0,X1] :
        ( ~ class_Ring__and__Field_Odvd(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f141,axiom,
    ! [X0,X1,X9] :
      ( ~ class_Ring__and__Field_Odvd(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvdI_0) ).

fof(f1238,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f140,f1236]) ).

fof(f1236,plain,
    ( spl0_89
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f140,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__triv__left_0) ).

fof(f1234,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f139,f1232]) ).

fof(f1232,plain,
    ( spl0_88
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f139,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__triv__right_0) ).

fof(f1230,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f137,f1228]) ).

fof(f1228,plain,
    ( spl0_87
  <=> ! [X5,X0,X6] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f137,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__le1_0) ).

fof(f1226,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f136,f1224]) ).

fof(f1224,plain,
    ( spl0_86
  <=> ! [X6,X0,X5] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f136,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_lessequals(c_Orderings_Oord__class_Omin(X5,X6,X0),X6,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__le2_0) ).

fof(f1222,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f114,f1220]) ).

fof(f114,axiom,
    ! [X3,X4] :
      ( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
      | ~ c_lessequals(c_Suc(X4),X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__eq__Suc__le_1) ).

fof(f1218,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f111,f1216]) ).

fof(f1216,plain,
    ( spl0_84
  <=> ! [X4,X3] :
        ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
        | c_lessequals(c_Suc(X3),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f111,axiom,
    ! [X3,X4] :
      ( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
      | c_lessequals(c_Suc(X3),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__leI_0) ).

fof(f1214,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f80,f1212]) ).

fof(f1212,plain,
    ( spl0_83
  <=> ! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f80,axiom,
    ! [X17] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X17,tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__nat__equiv__def2_1) ).

fof(f1210,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f18,f1208]) ).

fof(f1208,plain,
    ( spl0_82
  <=> ! [X4] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
        | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f18,axiom,
    ! [X4] :
      ( c_HOL_Ozero__class_Ozero(tc_nat) = X4
      | ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__0__eq_0) ).

fof(f1196,plain,
    ( spl0_81
    | ~ spl0_37
    | ~ spl0_75 ),
    inference(avatar_split_clause,[],[f1186,f1152,f988,f1193]) ).

fof(f1193,plain,
    ( spl0_81
  <=> c_lessequals(v_i,v_n,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1186,plain,
    ( c_lessequals(v_i,v_n,tc_nat)
    | ~ spl0_37
    | ~ spl0_75 ),
    inference(resolution,[],[f1153,f990]) ).

fof(f1174,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f735,f1172]) ).

fof(f1172,plain,
    ( spl0_80
  <=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f735,axiom,
    ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__less__Suc_0) ).

fof(f1170,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f713,f1168]) ).

fof(f1168,plain,
    ( spl0_79
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f713,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__0__eq__0_0) ).

fof(f1166,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f666,f1164]) ).

fof(f1164,plain,
    ( spl0_78
  <=> ! [X4,X3] :
        ( c_lessequals(X3,X4,tc_nat)
        | c_lessequals(X4,X3,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f666,axiom,
    ! [X3,X4] :
      ( c_lessequals(X3,X4,tc_nat)
      | c_lessequals(X4,X3,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__le__linear_0) ).

fof(f1162,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f575,f1160]) ).

fof(f1160,plain,
    ( spl0_77
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f575,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__is__0_1) ).

fof(f1158,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f574,f1156]) ).

fof(f574,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__is__0_2) ).

fof(f1154,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f562,f1152]) ).

fof(f562,axiom,
    ! [X6,X5] :
      ( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
      | c_lessequals(X5,X6,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_termination__basic__simps_I5_J_0) ).

fof(f1150,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f445,f1148]) ).

fof(f1148,plain,
    ( spl0_74
  <=> ! [X2,X0] :
        ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
        | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f445,axiom,
    ! [X2,X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
      | c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_abs__ge__self_0) ).

fof(f1146,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f443,f1144]) ).

fof(f1144,plain,
    ( spl0_73
  <=> ! [X29,X20] :
        ( X20 = X29
        | c_Suc(X20) != c_Suc(X29) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f443,axiom,
    ! [X29,X20] :
      ( X20 = X29
      | c_Suc(X20) != c_Suc(X29) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat_Oinject_0) ).

fof(f1142,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f320,f1140]) ).

fof(f1140,plain,
    ( spl0_72
  <=> ! [X4] :
        ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
        | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f320,axiom,
    ! [X4] :
      ( c_Parity_Oeven__odd__class_Oeven(X4,tc_nat)
      | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_odd__pos_0) ).

fof(f1138,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f186,f1136]) ).

fof(f1136,plain,
    ( spl0_71
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
        | c_HOL_Otimes__class_Otimes(X5,X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f186,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(X0)
      | c_HOL_Otimes__class_Otimes(X5,X5,X0) = X5 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mult__idem_0) ).

fof(f1134,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f121,f1132]) ).

fof(f1132,plain,
    ( spl0_70
  <=> ! [X5,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f121,axiom,
    ! [X3,X5] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__iff__Suc__add_1) ).

fof(f1130,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f120,f1128]) ).

fof(f1128,plain,
    ( spl0_69
  <=> ! [X8,X3] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f120,axiom,
    ! [X3,X8] : c_HOL_Oord__class_Oless(X8,c_Suc(c_HOL_Oplus__class_Oplus(X3,X8,tc_nat)),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_less__add__Suc2_0) ).

fof(f1126,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f88,f1124]) ).

fof(f1124,plain,
    ( spl0_68
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f88,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__0R_0) ).

fof(f1122,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f87,f1120]) ).

fof(f1120,plain,
    ( spl0_67
  <=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f87,axiom,
    ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__0L_0) ).

fof(f1118,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f16,f1116]) ).

fof(f16,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_min__max_Oinf__idem_0) ).

fof(f1103,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f716,f1101]) ).

fof(f1101,plain,
    ( spl0_65
  <=> ! [X4,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f716,axiom,
    ! [X3,X4] : c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__le__self_0) ).

fof(f1099,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f706,f1097]) ).

fof(f1097,plain,
    ( spl0_64
  <=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f706,axiom,
    ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_minus__nat_Odiff__0_0) ).

fof(f1095,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f705,f1093]) ).

fof(f1093,plain,
    ( spl0_63
  <=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f705,axiom,
    ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_diff__self__eq__0_0) ).

fof(f1091,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f598,f1089]) ).

fof(f1089,plain,
    ( spl0_62
  <=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f598,axiom,
    ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__add1_0) ).

fof(f1087,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f597,f1085]) ).

fof(f1085,plain,
    ( spl0_61
  <=> ! [X4,X3] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f597,axiom,
    ! [X3,X4] : c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__add2_0) ).

fof(f1083,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f568,f1081]) ).

fof(f1081,plain,
    ( spl0_60
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f568,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__0__right_0) ).

fof(f1079,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f559,f1077]) ).

fof(f1077,plain,
    ( spl0_59
  <=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f559,axiom,
    ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X8,tc_nat),X8,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__add__less2_0) ).

fof(f1075,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f558,f1073]) ).

fof(f1073,plain,
    ( spl0_58
  <=> ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f558,axiom,
    ! [X8,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),X8,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__add__less1_0) ).

fof(f1071,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f477,f1069]) ).

fof(f1069,plain,
    ( spl0_57
  <=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f477,axiom,
    ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_plus__nat_Oadd__0_0) ).

fof(f1067,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f475,f1065]) ).

fof(f1065,plain,
    ( spl0_56
  <=> ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f475,axiom,
    ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_natgb_Oadd__r0__iff_1) ).

fof(f1063,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f338,f1061]) ).

fof(f1061,plain,
    ( spl0_55
  <=> ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f338,axiom,
    ! [X3] : c_lessequals(X3,c_HOL_Otimes__class_Otimes(X3,X3,tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le__square_0) ).

fof(f1059,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f336,f1057]) ).

fof(f1057,plain,
    ( spl0_54
  <=> ! [X5] :
        ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
        | c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f336,axiom,
    ! [X5] :
      ( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__Suc_1) ).

fof(f1055,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f335,f1053]) ).

fof(f1053,plain,
    ( spl0_53
  <=> ! [X5] :
        ( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
        | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f335,axiom,
    ! [X5] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
      | ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X5),tc_nat) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__Suc_0) ).

fof(f1051,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f321,f1049]) ).

fof(f1049,plain,
    ( spl0_52
  <=> ! [X4,X3] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f321,axiom,
    ! [X3,X4] : c_lessequals(c_Divides_Odiv__class_Omod(X3,X4,tc_nat),X3,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_mod__less__eq__dividend_0) ).

fof(f1047,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f749,f1045]) ).

fof(f1045,plain,
    ( spl0_51
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f749,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__le_1) ).

fof(f1043,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f746,f1041]) ).

fof(f746,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_linorder__neq__iff_1) ).

fof(f1039,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f745,f1037]) ).

fof(f1037,plain,
    ( spl0_49
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f745,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__less__irrefl_0) ).

fof(f1035,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f637,f1033]) ).

fof(f1033,plain,
    ( spl0_48
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Oorder(X0)
        | c_lessequals(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f637,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Oorder(X0)
      | c_lessequals(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__eq__iff_0) ).

fof(f1031,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f636,f1029]) ).

fof(f1029,plain,
    ( spl0_47
  <=> ! [X5,X0] :
        ( ~ class_Orderings_Opreorder(X0)
        | c_lessequals(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f636,axiom,
    ! [X0,X5] :
      ( ~ class_Orderings_Opreorder(X0)
      | c_lessequals(X5,X5,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_order__eq__refl_0) ).

fof(f1027,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f305,f1025]) ).

fof(f1025,plain,
    ( spl0_46
  <=> ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f305,axiom,
    ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gr0__conv__Suc_1) ).

fof(f1023,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f277,f1021]) ).

fof(f1021,plain,
    ( spl0_45
  <=> ! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f277,axiom,
    ! [X9] : c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X9,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__1__left_0) ).

fof(f1019,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f35,f1017]) ).

fof(f1017,plain,
    ( spl0_44
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f35,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd__refl_0) ).

fof(f1015,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f681,f1013]) ).

fof(f681,axiom,
    ! [X4] : c_HOL_Oord__class_Oless(X4,c_Suc(X4),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_lessI_0) ).

fof(f1011,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f669,f1009]) ).

fof(f1009,plain,
    ( spl0_42
  <=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f669,axiom,
    ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_not__less0_0) ).

fof(f1007,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f623,f1005]) ).

fof(f1005,plain,
    ( spl0_41
  <=> ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f623,axiom,
    ! [X4] : ~ c_lessequals(c_Suc(X4),X4,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__n__not__le__n_0) ).

fof(f1003,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f567,f1001]) ).

fof(f1001,plain,
    ( spl0_40
  <=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f567,axiom,
    ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_gcd__lcm__complete__lattice__nat_Otop__greatest_0) ).

fof(f999,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f315,f997]) ).

fof(f997,plain,
    ( spl0_39
  <=> ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f315,axiom,
    ! [X4] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_le0_0) ).

fof(f995,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f127,f993]) ).

fof(f993,plain,
    ( spl0_38
  <=> ! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f127,axiom,
    ! [X20] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X20),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat_Osimps_I2_J_0) ).

fof(f991,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f767,f988]) ).

fof(f767,axiom,
    c_HOL_Oord__class_Oless(v_i,v_n,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_CHAINED_0) ).

fof(f986,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f747,f984]) ).

fof(f984,plain,
    ( spl0_36
  <=> ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f747,axiom,
    ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_nat__less__le_1) ).

fof(f982,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f638,f980]) ).

fof(f980,plain,
    ( spl0_35
  <=> ! [X5] : c_lessequals(X5,X5,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f638,axiom,
    ! [X5] : c_lessequals(X5,X5,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_eq__imp__le_0) ).

fof(f978,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f454,f975]) ).

fof(f975,plain,
    ( spl0_34
  <=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f454,axiom,
    c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_even__zero__nat_0) ).

fof(f973,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f185,f971]) ).

fof(f971,plain,
    ( spl0_33
  <=> ! [X4] : c_Suc(X4) != X4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f185,axiom,
    ! [X4] : c_Suc(X4) != X4,
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_Suc__n__not__n_0) ).

fof(f969,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f34,f967]) ).

fof(f967,plain,
    ( spl0_32
  <=> ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f34,axiom,
    ! [X5] : c_Ring__and__Field_Odvd__class_Odvd(X5,X5,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_dvd_Oeq__iff_0) ).

fof(f965,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f798,f962]) ).

fof(f962,plain,
    ( spl0_31
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f798,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Oorder) ).

fof(f960,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f797,f957]) ).

fof(f797,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Olinorder) ).

fof(f955,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f796,f952]) ).

fof(f952,plain,
    ( spl0_29
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f796,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Orderings_Opreorder) ).

fof(f950,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f795,f947]) ).

fof(f947,plain,
    ( spl0_28
  <=> class_Ring__and__Field_Odvd(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f795,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Odvd) ).

fof(f945,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f794,f942]) ).

fof(f942,plain,
    ( spl0_27
  <=> class_Nat_Osemiring__char__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f794,axiom,
    class_Nat_Osemiring__char__0(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Nat_Osemiring__char__0) ).

fof(f940,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f793,f937]) ).

fof(f937,plain,
    ( spl0_26
  <=> class_Divides_Osemiring__div(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f793,axiom,
    class_Divides_Osemiring__div(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Divides_Osemiring__div) ).

fof(f935,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f792,f932]) ).

fof(f932,plain,
    ( spl0_25
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f792,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f930,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f791,f927]) ).

fof(f927,plain,
    ( spl0_24
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f791,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f925,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f790,f922]) ).

fof(f922,plain,
    ( spl0_23
  <=> class_Ring__and__Field_Omult__mono(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f790,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__mono) ).

fof(f920,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f789,f917]) ).

fof(f917,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f789,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f915,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f788,f912]) ).

fof(f912,plain,
    ( spl0_21
  <=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f788,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Omult__mono1) ).

fof(f910,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f787,f907]) ).

fof(f907,plain,
    ( spl0_20
  <=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f787,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Osemiring__1) ).

fof(f905,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f786,f902]) ).

fof(f902,plain,
    ( spl0_19
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f786,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f900,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f785,f897]) ).

fof(f897,plain,
    ( spl0_18
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f785,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f895,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f784,f892]) ).

fof(f892,plain,
    ( spl0_17
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f784,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f890,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f783,f887]) ).

fof(f887,plain,
    ( spl0_16
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f783,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f885,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f782,f882]) ).

fof(f882,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f782,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f880,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f781,f877]) ).

fof(f877,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f781,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

fof(f875,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f780,f872]) ).

fof(f872,plain,
    ( spl0_13
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f780,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

fof(f870,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f779,f867]) ).

fof(f867,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f779,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

fof(f865,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f778,f862]) ).

fof(f862,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f778,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

fof(f860,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f777,f857]) ).

fof(f857,plain,
    ( spl0_10
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f777,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f855,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f776,f852]) ).

fof(f852,plain,
    ( spl0_9
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f776,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f850,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f775,f847]) ).

fof(f847,plain,
    ( spl0_8
  <=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f775,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

fof(f845,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f774,f842]) ).

fof(f842,plain,
    ( spl0_7
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f774,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f840,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f773,f837]) ).

fof(f837,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f773,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

fof(f835,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f772,f832]) ).

fof(f832,plain,
    ( spl0_5
  <=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f772,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

fof(f830,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f771,f827]) ).

fof(f827,plain,
    ( spl0_4
  <=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f771,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

fof(f825,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f770,f822]) ).

fof(f822,plain,
    ( spl0_3
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f770,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f820,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f769,f817]) ).

fof(f817,plain,
    ( spl0_2
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f769,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f815,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f768,f812]) ).

fof(f768,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_i,v_k,tc_nat),v_n,tc_nat),
    file('/export/starexec/sandbox/tmp/tmp.XSYuOgkCFE/Vampire---4.8_25132',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.19  % Problem    : SWV689-1 : TPTP v8.1.2. Released v4.1.0.
% 0.19/0.20  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.21/0.41  % Computer : n024.cluster.edu
% 0.21/0.41  % Model    : x86_64 x86_64
% 0.21/0.41  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.41  % Memory   : 8042.1875MB
% 0.21/0.41  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.21/0.41  % CPULimit   : 300
% 0.21/0.41  % WCLimit    : 300
% 0.21/0.41  % DateTime   : Wed Aug 30 17:43:07 EDT 2023
% 0.21/0.42  % CPUTime    : 
% 0.28/0.47  % (25329)Running in auto input_syntax mode. Trying TPTP
% 0.28/0.51  % (25331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.28/0.51  % (25332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.28/0.51  % (25333)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 Vampire---4 for (569ds/0Mi)
% 0.28/0.51  % (25334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.28/0.51  % (25335)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 Vampire---4 for (531ds/0Mi)
% 0.28/0.51  % (25336)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 Vampire---4 for (522ds/0Mi)
% 0.28/0.51  % (25337)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 Vampire---4 for (497ds/0Mi)
% 0.28/0.57  % (25335)First to succeed.
% 0.28/0.58  % (25335)Refutation found. Thanks to Tanya!
% 0.28/0.58  % SZS status Unsatisfiable for Vampire---4
% 0.28/0.58  % SZS output start Proof for Vampire---4
% See solution above
% 0.28/0.59  % (25335)------------------------------
% 0.28/0.59  % (25335)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.28/0.59  % (25335)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.28/0.59  % (25335)Termination reason: Refutation
% 0.28/0.59  
% 0.28/0.59  % (25335)Memory used [KB]: 7675
% 0.28/0.59  % (25335)Time elapsed: 0.071 s
% 0.28/0.59  % (25335)------------------------------
% 0.28/0.59  % (25335)------------------------------
% 0.28/0.59  % (25329)Success in time 0.159 s
% 0.28/0.59  % Vampire---4.8 exiting
%------------------------------------------------------------------------------