TSTP Solution File: SWV844-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV844-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 11:11:56 EDT 2024

% Result   : Unsatisfiable 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  316
% Syntax   : Number of formulae    :  495 ( 236 unt;   0 def)
%            Number of atoms       :  861 ( 106 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  604 ( 238   ~; 205   |;   0   &)
%                                         ( 161 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :  199 ( 197 usr; 162 prp; 0-6 aty)
%            Number of functors    :   44 (  44 usr;  15 con; 0-5 aty)
%            Number of variables   :  533 ( 533   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1835,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1059,f1064,f1069,f1074,f1079,f1084,f1089,f1094,f1099,f1104,f1109,f1114,f1119,f1124,f1129,f1134,f1139,f1144,f1149,f1154,f1159,f1164,f1169,f1174,f1179,f1184,f1189,f1194,f1199,f1204,f1209,f1214,f1219,f1224,f1229,f1234,f1239,f1244,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1325,f1329,f1333,f1337,f1342,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1420,f1424,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1497,f1508,f1512,f1516,f1520,f1525,f1529,f1533,f1537,f1541,f1545,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1616,f1625,f1629,f1633,f1637,f1642,f1646,f1650,f1654,f1658,f1662,f1666,f1670,f1696,f1700,f1705,f1709,f1713,f1717,f1721,f1725,f1729,f1733,f1737,f1741,f1750,f1754,f1779,f1783,f1789,f1793,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1834]) ).

fof(f1834,plain,
    ( spl0_63
    | ~ spl0_62
    | ~ spl0_149 ),
    inference(avatar_split_clause,[],[f1785,f1781,f1339,f1344]) ).

fof(f1344,plain,
    ( spl0_63
  <=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1339,plain,
    ( spl0_62
  <=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1781,plain,
    ( spl0_149
  <=> ! [X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
        | c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f1785,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
    | ~ spl0_62
    | ~ spl0_149 ),
    inference(resolution,[],[f1782,f1341]) ).

fof(f1341,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f1339]) ).

fof(f1782,plain,
    ( ! [X65] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
        | c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1781]) ).

fof(f1833,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f716,f1831]) ).

fof(f1831,plain,
    ( spl0_161
  <=> ! [X0,X14,X15] :
        ( ~ c_Finite__Set_Ofinite(X14,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X14),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f716,axiom,
    ! [X0,X14,X15] :
      ( ~ c_Finite__Set_Ofinite(X14,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(X0,tc_bool)),X14),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

fof(f1829,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f711,f1827]) ).

fof(f1827,plain,
    ( spl0_160
  <=> ! [X0,X44,X42] :
        ( c_Finite__Set_Ofinite(X42,X0)
        | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f711,axiom,
    ! [X0,X44,X42] :
      ( c_Finite__Set_Ofinite(X42,X0)
      | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).

fof(f1825,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f710,f1823]) ).

fof(f1823,plain,
    ( spl0_159
  <=> ! [X0,X44,X42] :
        ( c_Finite__Set_Ofinite(X44,X0)
        | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f710,axiom,
    ! [X0,X44,X42] :
      ( c_Finite__Set_Ofinite(X44,X0)
      | ~ c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X42),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).

fof(f1821,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f564,f1819]) ).

fof(f1819,plain,
    ( spl0_158
  <=> ! [X17,X13,X0,X3,X28] :
        ( X3 = X17
        | ~ c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f564,axiom,
    ! [X3,X28,X0,X17,X13] :
      ( X3 = X17
      | ~ c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3,X0,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).

fof(f1817,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f562,f1815]) ).

fof(f1815,plain,
    ( spl0_157
  <=> ! [X13,X0,X17,X28] : hAPP(hAPP(c_Finite__Set_Ofold(X28,X13,X0),X17),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))) = X17 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f562,axiom,
    ! [X28,X0,X17,X13] : hAPP(hAPP(c_Finite__Set_Ofold(X28,X13,X0),X17),c_Orderings_Obot__class_Obot(tc_fun(X13,tc_bool))) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__empty_0) ).

fof(f1813,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f558,f1811]) ).

fof(f1811,plain,
    ( spl0_156
  <=> ! [X0,X44,X42] :
        ( ~ c_Finite__Set_Ofinite(X42,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f558,axiom,
    ! [X0,X44,X42] :
      ( ~ c_Finite__Set_Ofinite(X42,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

fof(f1809,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f557,f1807]) ).

fof(f1807,plain,
    ( spl0_155
  <=> ! [X0,X44,X42] :
        ( ~ c_Finite__Set_Ofinite(X44,X0)
        | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f557,axiom,
    ! [X0,X44,X42] :
      ( ~ c_Finite__Set_Ofinite(X44,X0)
      | c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X42),X44),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

fof(f1805,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f523,f1803]) ).

fof(f1803,plain,
    ( spl0_154
  <=> ! [X0,X14] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X14)) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f523,axiom,
    ! [X0,X14] : hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_fun(X0,tc_bool)),X14)) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).

fof(f1801,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f516,f1799]) ).

fof(f1799,plain,
    ( spl0_153
  <=> ! [X3,X13,X0,X5,X28] :
        ( hAPP(X28,X3) = X5
        | c_Fun_Ofun__upd(X28,X3,X5,X0,X13) != X28 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f516,axiom,
    ! [X28,X3,X0,X5,X13] :
      ( hAPP(X28,X3) = X5
      | c_Fun_Ofun__upd(X28,X3,X5,X0,X13) != X28 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

fof(f1797,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f174,f1795]) ).

fof(f1795,plain,
    ( spl0_152
  <=> ! [X18,X21] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),c_Suc(X18))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f174,axiom,
    ! [X21,X18] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),c_Suc(X18))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

fof(f1793,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f54,f1791]) ).

fof(f1791,plain,
    ( spl0_151
  <=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f54,axiom,
    ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

fof(f1789,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f53,f1787]) ).

fof(f1787,plain,
    ( spl0_150
  <=> ! [X0,X15] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X15) = X15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f53,axiom,
    ! [X0,X15] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),X15) = X15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

fof(f1783,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f984,f1781]) ).

fof(f984,axiom,
    ! [X65] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,X65)),hAPP(v_c0,X65)),hAPP(v_Q_H,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b)
      | c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,X65)),hAPP(v_c0,X65)),hAPP(v_Q,X65)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f1779,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f982,f1776]) ).

fof(f1776,plain,
    ( spl0_148
  <=> c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f982,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),v_P_H,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q_H,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),v_F,t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f1754,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f950,f1752]) ).

fof(f1752,plain,
    ( spl0_147
  <=> ! [X3,X0,X14] : c_Set_Oinsert(X3,X14,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X14,X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f950,axiom,
    ! [X3,X0,X14] : c_Set_Oinsert(X3,X14,X0) = c_Set_Oinsert(X3,c_Set_Oinsert(X3,X14,X0),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f1750,plain,
    ( spl0_145
    | ~ spl0_146
    | ~ spl0_26
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f1486,f1418,f1181,f1747,f1743]) ).

fof(f1743,plain,
    ( spl0_145
  <=> c_Orderings_Oord__class_Omax(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f1747,plain,
    ( spl0_146
  <=> class_Orderings_Olinorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1181,plain,
    ( spl0_26
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f1418,plain,
    ( spl0_81
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ class_Lattices_Oupper__semilattice(X0)
        | c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1486,plain,
    ( ~ class_Orderings_Olinorder(tc_bool)
    | c_Orderings_Oord__class_Omax(tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(tc_bool)
    | ~ spl0_26
    | ~ spl0_81 ),
    inference(resolution,[],[f1419,f1183]) ).

fof(f1183,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f1181]) ).

fof(f1419,plain,
    ( ! [X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | ~ class_Orderings_Olinorder(X0)
        | c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) )
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f1418]) ).

fof(f1741,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f928,f1739]) ).

fof(f1739,plain,
    ( spl0_144
  <=> ! [X44,X57,X0,X56] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X0)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,X57,X0)
        | c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f928,axiom,
    ! [X0,X56,X57,X44] :
      ( ~ c_Hoare__Mirabelle_Ohoare__derivs(X57,X56,X0)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,X57,X0)
      | c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).

fof(f1737,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f920,f1735]) ).

fof(f1735,plain,
    ( spl0_143
  <=> ! [X44,X0,X56,X45] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Set_Oinsert(X45,X56,tc_Hoare__Mirabelle_Otriple(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f920,axiom,
    ! [X0,X56,X44,X45] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(X44,X56,X0)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Set_Oinsert(X45,X56,tc_Hoare__Mirabelle_Otriple(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).

fof(f1733,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f845,f1731]) ).

fof(f1731,plain,
    ( spl0_142
  <=> ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f845,axiom,
    ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X14),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

fof(f1729,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f807,f1727]) ).

fof(f1727,plain,
    ( spl0_141
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f807,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Otop__class_Otop(X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).

fof(f1725,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f806,f1723]) ).

fof(f1723,plain,
    ( spl0_140
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f806,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Otop__class_Otop(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).

fof(f1721,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f745,f1719]) ).

fof(f1719,plain,
    ( spl0_139
  <=> ! [X0,X1,X15] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X15),c_Set_Oinsert(X1,X15,X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f745,axiom,
    ! [X0,X1,X15] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X15),c_Set_Oinsert(X1,X15,X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1717,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f734,f1715]) ).

fof(f1715,plain,
    ( spl0_138
  <=> ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f734,axiom,
    ! [X0,X14] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))),X14)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1713,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f563,f1711]) ).

fof(f1711,plain,
    ( spl0_137
  <=> ! [X0,X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f563,axiom,
    ! [X0,X14] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X14),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

fof(f1709,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f560,f1707]) ).

fof(f1707,plain,
    ( spl0_136
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f560,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Obot__class_Obot(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f1705,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f559,f1703]) ).

fof(f1703,plain,
    ( spl0_135
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f559,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Obot__class_Obot(X0)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f1700,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f347,f1698]) ).

fof(f1698,plain,
    ( spl0_134
  <=> ! [X18,X21] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),X18)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f347,axiom,
    ! [X21,X18] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_nat),X18),X21)),X18)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

fof(f1696,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f131,f1694]) ).

fof(f1694,plain,
    ( spl0_133
  <=> ! [X4,X0,X6,X3,X7] :
        ( ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0)
        | hAPP(hAPP(X4,X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f131,axiom,
    ! [X3,X0,X6,X7,X4] :
      ( ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0)
      | hAPP(hAPP(X4,X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oinf__idem_0) ).

fof(f1670,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f972,f1668]) ).

fof(f1668,plain,
    ( spl0_132
  <=> ! [X0,X1,X14] :
        ( ~ hBOOL(c_in(X1,X14,X0))
        | c_Set_Oinsert(X1,X14,X0) = X14 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f972,axiom,
    ! [X0,X1,X14] :
      ( ~ hBOOL(c_in(X1,X14,X0))
      | c_Set_Oinsert(X1,X14,X0) = X14 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f1666,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f969,f1664]) ).

fof(f1664,plain,
    ( spl0_131
  <=> ! [X5,X0,X3,X14] :
        ( ~ hBOOL(hAPP(X14,X3))
        | hBOOL(hAPP(c_Set_Oinsert(X5,X14,X0),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f969,axiom,
    ! [X3,X0,X14,X5] :
      ( ~ hBOOL(hAPP(X14,X3))
      | hBOOL(hAPP(c_Set_Oinsert(X5,X14,X0),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f1662,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f953,f1660]) ).

fof(f1660,plain,
    ( spl0_130
  <=> ! [X13] :
        ( ~ class_Orderings_Obot(X13)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X13)),v_x) = c_Orderings_Obot__class_Obot(X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f953,axiom,
    ! [X13] :
      ( ~ class_Orderings_Obot(X13)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X13)),v_x) = c_Orderings_Obot__class_Obot(X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f1658,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f848,f1656]) ).

fof(f1656,plain,
    ( spl0_129
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f848,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__empty_0) ).

fof(f1654,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f826,f1652]) ).

fof(f1652,plain,
    ( spl0_128
  <=> ! [X13] :
        ( ~ class_Orderings_Otop(X13)
        | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X13)),v_x) = c_Orderings_Otop__class_Otop(X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f826,axiom,
    ! [X13] :
      ( ~ class_Orderings_Otop(X13)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,X13)),v_x) = c_Orderings_Otop__class_Otop(X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).

fof(f1650,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f824,f1648]) ).

fof(f1648,plain,
    ( spl0_127
  <=> ! [X0] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
        | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f824,axiom,
    ! [X0] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X0)
      | c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).

fof(f1646,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f718,f1644]) ).

fof(f1644,plain,
    ( spl0_126
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f718,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),c_Orderings_Obot__class_Obot(X0)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1642,plain,
    ( ~ spl0_125
    | ~ spl0_73
    | ~ spl0_117 ),
    inference(avatar_split_clause,[],[f1620,f1579,f1385,f1639]) ).

fof(f1639,plain,
    ( spl0_125
  <=> class_Orderings_Otop(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f1385,plain,
    ( spl0_73
  <=> ! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f1579,plain,
    ( spl0_117
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Otop(X0)
        | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f1620,plain,
    ( ~ class_Orderings_Otop(tc_nat)
    | ~ spl0_73
    | ~ spl0_117 ),
    inference(resolution,[],[f1580,f1386]) ).

fof(f1386,plain,
    ( ! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21))
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f1385]) ).

fof(f1580,plain,
    ( ! [X3,X0] :
        ( hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0)))
        | ~ class_Orderings_Otop(X0) )
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f1579]) ).

fof(f1637,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f717,f1635]) ).

fof(f1635,plain,
    ( spl0_124
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f717,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),c_Orderings_Obot__class_Obot(X0)),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1633,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f525,f1631]) ).

fof(f1631,plain,
    ( spl0_123
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f525,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | hAPP(c_HOL_Ouminus__class_Ouminus(X0),hAPP(c_HOL_Ouminus__class_Ouminus(X0),X3)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

fof(f1629,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f52,f1627]) ).

fof(f1627,plain,
    ( spl0_122
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f52,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),c_Orderings_Otop__class_Otop(X0)),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

fof(f1625,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f51,f1623]) ).

fof(f1623,plain,
    ( spl0_121
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Obounded__lattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f51,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Obounded__lattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),c_Orderings_Otop__class_Otop(X0)) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

fof(f1616,plain,
    ( ~ spl0_13
    | spl0_120
    | ~ spl0_45
    | ~ spl0_98 ),
    inference(avatar_split_clause,[],[f1597,f1494,f1271,f1613,f1116]) ).

fof(f1116,plain,
    ( spl0_13
  <=> class_Lattices_Oupper__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1613,plain,
    ( spl0_120
  <=> c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1271,plain,
    ( spl0_45
  <=> ! [X0] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f1494,plain,
    ( spl0_98
  <=> c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f1597,plain,
    ( c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(tc_nat),tc_nat)
    | ~ class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_45
    | ~ spl0_98 ),
    inference(superposition,[],[f1272,f1496]) ).

fof(f1496,plain,
    ( c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat)
    | ~ spl0_98 ),
    inference(avatar_component_clause,[],[f1494]) ).

fof(f1272,plain,
    ( ! [X0] :
        ( c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0)
        | ~ class_Lattices_Oupper__semilattice(X0) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f1271]) ).

fof(f1589,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f1042,f1587]) ).

fof(f1587,plain,
    ( spl0_119
  <=> ! [X69,X0,X68] :
        ( X68 = X69
        | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X68),X69)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f1042,axiom,
    ! [X0,X68,X69] :
      ( X68 = X69
      | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X68),X69)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1585,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f942,f1583]) ).

fof(f1583,plain,
    ( spl0_118
  <=> ! [X13,X48,X0,X42] :
        ( ~ c_Finite__Set_Ofinite(X42,X0)
        | c_Finite__Set_Ofinite(c_Set_Oimage(X48,X42,X0,X13),X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f942,axiom,
    ! [X48,X0,X42,X13] :
      ( ~ c_Finite__Set_Ofinite(X42,X0)
      | c_Finite__Set_Ofinite(c_Set_Oimage(X48,X42,X0,X13),X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

fof(f1581,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f846,f1579]) ).

fof(f846,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Otop(X0)
      | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),c_Orderings_Otop__class_Otop(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

fof(f1577,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f804,f1575]) ).

fof(f1575,plain,
    ( spl0_116
  <=> ! [X51,X50,X49,X52] :
        ( X49 = X51
        | c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f804,axiom,
    ! [X50,X51,X49,X52] :
      ( X49 = X51
      | c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).

fof(f1573,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f803,f1571]) ).

fof(f1571,plain,
    ( spl0_115
  <=> ! [X52,X50,X51,X49] :
        ( X50 = X52
        | c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f803,axiom,
    ! [X50,X51,X49,X52] :
      ( X50 = X52
      | c_Com_Ocom_OSemi(X49,X50) != c_Com_Ocom_OSemi(X51,X52) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).

fof(f1569,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f794,f1567]) ).

fof(f1567,plain,
    ( spl0_114
  <=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X14) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f794,axiom,
    ! [X0,X14] : hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(X0,tc_bool)),X14),X14) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f1565,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f793,f1563]) ).

fof(f1563,plain,
    ( spl0_113
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f793,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X0),X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1561,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f719,f1559]) ).

fof(f1559,plain,
    ( spl0_112
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Obot(X0)
        | hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f719,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Obot(X0)
      | hBOOL(hAPP(hAPP(c_lessequals(X0),c_Orderings_Obot__class_Obot(X0)),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f1557,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f568,f1555]) ).

fof(f1555,plain,
    ( spl0_111
  <=> ! [X13,X0,X17,X28] : c_Nitpick_Ofold__graph_H(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f568,axiom,
    ! [X28,X0,X17,X13] : c_Nitpick_Ofold__graph_H(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).

fof(f1553,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f567,f1551]) ).

fof(f1551,plain,
    ( spl0_110
  <=> ! [X13,X0,X17,X28] : c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f567,axiom,
    ! [X28,X0,X17,X13] : c_Finite__Set_Ofold__graph(X28,X17,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X17,X0,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).

fof(f1549,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f556,f1547]) ).

fof(f1547,plain,
    ( spl0_109
  <=> ! [X17,X13,X0,X14,X3,X28] :
        ( c_Finite__Set_Ofinite(X14,X0)
        | ~ c_Finite__Set_Ofold__graph(X28,X17,X14,X3,X0,X13) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f556,axiom,
    ! [X28,X3,X0,X14,X17,X13] :
      ( c_Finite__Set_Ofinite(X14,X0)
      | ~ c_Finite__Set_Ofold__graph(X28,X17,X14,X3,X0,X13) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).

fof(f1545,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f466,f1543]) ).

fof(f1543,plain,
    ( spl0_108
  <=> ! [X0] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f466,axiom,
    ! [X0] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_Orderings_Otop__class_Otop(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__bot__eq_0) ).

fof(f1541,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f465,f1539]) ).

fof(f1539,plain,
    ( spl0_107
  <=> ! [X0] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f465,axiom,
    ! [X0] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_Orderings_Obot__class_Obot(X0) = hAPP(c_HOL_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__top__eq_0) ).

fof(f1537,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f253,f1535]) ).

fof(f1535,plain,
    ( spl0_106
  <=> ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),X14) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f253,axiom,
    ! [X0,X14] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X14),X14) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1533,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f252,f1531]) ).

fof(f1531,plain,
    ( spl0_105
  <=> ! [X0,X3] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f252,axiom,
    ! [X3,X0] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(X0),X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1529,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f211,f1527]) ).

fof(f1527,plain,
    ( spl0_104
  <=> ! [X28,X34,X0,X5,X3] : hAPP(c_Fun_Ofun__upd(X28,X3,X5,X0,X34),X3) = X5 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f211,axiom,
    ! [X28,X3,X0,X34,X5] : hAPP(c_Fun_Ofun__upd(X28,X3,X5,X0,X34),X3) = X5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

fof(f1525,plain,
    ( ~ spl0_103
    | spl0_2
    | ~ spl0_96 ),
    inference(avatar_split_clause,[],[f1500,f1478,f1061,f1522]) ).

fof(f1522,plain,
    ( spl0_103
  <=> hBOOL(hAPP(v_F,v_x)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1061,plain,
    ( spl0_2
  <=> hBOOL(c_in(v_x,v_F,t_a)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1478,plain,
    ( spl0_96
  <=> ! [X64,X0,X3] :
        ( ~ hBOOL(hAPP(X64,X3))
        | hBOOL(c_in(X3,X64,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1500,plain,
    ( ~ hBOOL(hAPP(v_F,v_x))
    | spl0_2
    | ~ spl0_96 ),
    inference(resolution,[],[f1479,f1063]) ).

fof(f1063,plain,
    ( ~ hBOOL(c_in(v_x,v_F,t_a))
    | spl0_2 ),
    inference(avatar_component_clause,[],[f1061]) ).

fof(f1479,plain,
    ( ! [X3,X0,X64] :
        ( hBOOL(c_in(X3,X64,X0))
        | ~ hBOOL(hAPP(X64,X3)) )
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f1478]) ).

fof(f1520,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f210,f1518]) ).

fof(f1518,plain,
    ( spl0_102
  <=> ! [X13,X0,X3,X28] : c_Fun_Ofun__upd(X28,X3,hAPP(X28,X3),X0,X13) = X28 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f210,axiom,
    ! [X28,X3,X0,X13] : c_Fun_Ofun__upd(X28,X3,hAPP(X28,X3),X0,X13) = X28,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

fof(f1516,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f83,f1514]) ).

fof(f1514,plain,
    ( spl0_101
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f83,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X0),X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).

fof(f1512,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f73,f1510]) ).

fof(f1510,plain,
    ( spl0_100
  <=> ! [X0,X3,X31] :
        ( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X31,X0)
        | hAPP(hAPP(X31,X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f73,axiom,
    ! [X31,X3,X0] :
      ( ~ c_OrderedGroup_Oab__semigroup__idem__mult(X31,X0)
      | hAPP(hAPP(X31,X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult_Omult__idem_0) ).

fof(f1508,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f66,f1506]) ).

fof(f1506,plain,
    ( spl0_99
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f66,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X0),X3),X3) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).

fof(f1497,plain,
    ( spl0_98
    | ~ spl0_19
    | ~ spl0_13
    | ~ spl0_81 ),
    inference(avatar_split_clause,[],[f1485,f1418,f1116,f1146,f1494]) ).

fof(f1146,plain,
    ( spl0_19
  <=> class_Orderings_Olinorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f1485,plain,
    ( ~ class_Orderings_Olinorder(tc_nat)
    | c_Orderings_Oord__class_Omax(tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(tc_nat)
    | ~ spl0_13
    | ~ spl0_81 ),
    inference(resolution,[],[f1419,f1118]) ).

fof(f1118,plain,
    ( class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f1116]) ).

fof(f1484,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f960,f1482]) ).

fof(f1482,plain,
    ( spl0_97
  <=> ! [X64,X0,X3] :
        ( hBOOL(hAPP(X64,X3))
        | ~ hBOOL(c_in(X3,X64,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f960,axiom,
    ! [X3,X0,X64] :
      ( hBOOL(hAPP(X64,X3))
      | ~ hBOOL(c_in(X3,X64,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1480,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f959,f1478]) ).

fof(f959,axiom,
    ! [X3,X0,X64] :
      ( ~ hBOOL(hAPP(X64,X3))
      | hBOOL(c_in(X3,X64,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1476,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f951,f1474]) ).

fof(f1474,plain,
    ( spl0_95
  <=> ! [X0,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X14,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f951,axiom,
    ! [X0,X1,X14] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Set_Oinsert(X1,X14,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

fof(f1472,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f948,f1470]) ).

fof(f1470,plain,
    ( spl0_94
  <=> ! [X0,X1,X14] :
        ( c_Finite__Set_Ofinite(X14,X0)
        | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f948,axiom,
    ! [X0,X1,X14] :
      ( c_Finite__Set_Ofinite(X14,X0)
      | ~ c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

fof(f1468,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f947,f1466]) ).

fof(f1466,plain,
    ( spl0_93
  <=> ! [X0,X1,X14] :
        ( ~ c_Finite__Set_Ofinite(X14,X0)
        | c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f947,axiom,
    ! [X0,X1,X14] :
      ( ~ c_Finite__Set_Ofinite(X14,X0)
      | c_Finite__Set_Ofinite(c_Set_Oinsert(X1,X14,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

fof(f1464,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f865,f1462]) ).

fof(f1462,plain,
    ( spl0_92
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Opreorder(X0)
        | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f865,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Opreorder(X0)
      | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f1460,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f864,f1458]) ).

fof(f1458,plain,
    ( spl0_91
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f864,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | hBOOL(hAPP(hAPP(c_lessequals(X0),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f1456,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f859,f1454]) ).

fof(f1454,plain,
    ( spl0_90
  <=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f859,axiom,
    ! [X3,X0] : hBOOL(hAPP(hAPP(c_lessequals(tc_fun(X0,tc_bool)),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

fof(f1452,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f728,f1450]) ).

fof(f1450,plain,
    ( spl0_89
  <=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f728,axiom,
    ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

fof(f1448,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f496,f1446]) ).

fof(f1446,plain,
    ( spl0_88
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f496,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omin(X0),X0) = c_Finite__Set_Olinorder__class_OMin(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__class_OMin__def__raw_0) ).

fof(f1444,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f495,f1442]) ).

fof(f1442,plain,
    ( spl0_87
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f495,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_Finite__Set_Olinorder__class_OMax(X0) = c_Finite__Set_Ofold1(c_Orderings_Oord__class_Omax(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__def__raw_0) ).

fof(f1440,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f196,f1438]) ).

fof(f1438,plain,
    ( spl0_86
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ class_Lattices_Olower__semilattice(X0)
        | c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f196,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ class_Lattices_Olower__semilattice(X0)
      | c_Orderings_Oord__class_Omin(X0) = c_Lattices_Olower__semilattice__class_Oinf(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).

fof(f1436,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f64,f1434]) ).

fof(f1434,plain,
    ( spl0_85
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Opreorder(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f64,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Opreorder(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

fof(f1432,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f63,f1430]) ).

fof(f1430,plain,
    ( spl0_84
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Olinorder(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f63,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

fof(f1428,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f62,f1426]) ).

fof(f1426,plain,
    ( spl0_83
  <=> ! [X0,X3] :
        ( ~ class_Orderings_Oorder(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f62,axiom,
    ! [X3,X0] :
      ( ~ class_Orderings_Oorder(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(X0),X3),X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

fof(f1424,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f58,f1422]) ).

fof(f1422,plain,
    ( spl0_82
  <=> ! [X0,X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f58,axiom,
    ! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(X0,tc_bool)),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

fof(f1420,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f32,f1418]) ).

fof(f32,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | ~ class_Lattices_Oupper__semilattice(X0)
      | c_Orderings_Oord__class_Omax(X0) = c_Lattices_Oupper__semilattice__class_Osup(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__max_0) ).

fof(f1415,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f992,f1413]) ).

fof(f1413,plain,
    ( spl0_80
  <=> ! [X66,X67] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X66)
        | ~ class_Finite__Set_Ofinite_Ofinite(X67)
        | class_Finite__Set_Ofinite_Ofinite(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f992,axiom,
    ! [X66,X67] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X66)
      | ~ class_Finite__Set_Ofinite_Ofinite(X67)
      | class_Finite__Set_Ofinite_Ofinite(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

fof(f1411,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f956,f1409]) ).

fof(f1409,plain,
    ( spl0_79
  <=> ! [X0,X1,X15] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X15,X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f956,axiom,
    ! [X0,X1,X15] : hBOOL(c_in(X1,c_Set_Oinsert(X1,X15,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

fof(f1407,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f945,f1405]) ).

fof(f1405,plain,
    ( spl0_78
  <=> ! [X0,X44] : c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f945,axiom,
    ! [X0,X44] : c_Hoare__Mirabelle_Ohoare__derivs(X44,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X0),tc_bool)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).

fof(f1403,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f931,f1401]) ).

fof(f1401,plain,
    ( spl0_77
  <=> ! [X0,X11] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f931,axiom,
    ! [X0,X11] : ~ hBOOL(c_in(X11,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

fof(f1399,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f792,f1397]) ).

fof(f1397,plain,
    ( spl0_76
  <=> ! [X40,X13,X0,X32] : hAPP(c_COMBK(X32,X0,X13),X40) = X32 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f792,axiom,
    ! [X40,X0,X32,X13] : hAPP(c_COMBK(X32,X0,X13),X40) = X32,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1395,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f735,f1393]) ).

fof(f1393,plain,
    ( spl0_75
  <=> ! [X13,X0,X28] : c_Fun_Oinj__on(X28,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f735,axiom,
    ! [X28,X0,X13] : c_Fun_Oinj__on(X28,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

fof(f1391,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f690,f1389]) ).

fof(f1389,plain,
    ( spl0_74
  <=> ! [X0,X3] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f690,axiom,
    ! [X3,X0] : hBOOL(c_in(X3,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

fof(f1387,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f244,f1385]) ).

fof(f244,axiom,
    ! [X21] : ~ hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Suc(X21)),X21)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

fof(f1383,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f213,f1381]) ).

fof(f1381,plain,
    ( spl0_72
  <=> ! [X6,X4,X0,X7] :
        ( c_OrderedGroup_Oab__semigroup__idem__mult(X4,X0)
        | ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f213,axiom,
    ! [X0,X6,X7,X4] :
      ( c_OrderedGroup_Oab__semigroup__idem__mult(X4,X0)
      | ~ c_Lattices_Olower__semilattice(X6,X7,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lower__semilattice_Oab__semigroup__idem__mult__inf_0) ).

fof(f1379,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f198,f1377]) ).

fof(f1377,plain,
    ( spl0_71
  <=> ! [X3] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),c_Suc(X3))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f198,axiom,
    ! [X3] : hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),c_Suc(X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

fof(f1375,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f8,f1373]) ).

fof(f1373,plain,
    ( spl0_70
  <=> ! [X9,X8] :
        ( X8 = X9
        | c_Suc(X8) != c_Suc(X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f8,axiom,
    ! [X8,X9] :
      ( X8 = X9
      | c_Suc(X8) != c_Suc(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

fof(f1371,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f1041,f1369]) ).

fof(f1369,plain,
    ( spl0_69
  <=> ! [X0,X3] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f1041,axiom,
    ! [X3,X0] : hBOOL(hAPP(hAPP(c_fequal(X0),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f1367,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f944,f1365]) ).

fof(f1365,plain,
    ( spl0_68
  <=> ! [X0,X3] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f944,axiom,
    ! [X3,X0] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f1363,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f926,f1361]) ).

fof(f1361,plain,
    ( spl0_67
  <=> ! [X0,X3,X14] : hBOOL(hAPP(c_Set_Oinsert(X3,X14,X0),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f926,axiom,
    ! [X3,X0,X14] : hBOOL(hAPP(c_Set_Oinsert(X3,X14,X0),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f1359,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f825,f1357]) ).

fof(f1357,plain,
    ( spl0_66
  <=> ! [X0,X3] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f825,axiom,
    ! [X3,X0] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

fof(f1355,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f266,f1353]) ).

fof(f1353,plain,
    ( spl0_65
  <=> ! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f266,axiom,
    ! [X3] : hBOOL(hAPP(hAPP(c_lessequals(tc_nat),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

fof(f1351,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f59,f1349]) ).

fof(f1349,plain,
    ( spl0_64
  <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f59,axiom,
    ! [X3] : ~ hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

fof(f1347,plain,
    ~ spl0_63,
    inference(avatar_split_clause,[],[f983,f1344]) ).

fof(f983,axiom,
    ~ c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f1342,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f981,f1339]) ).

fof(f981,axiom,
    c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_P_H,v_x)),hAPP(v_c0,v_x)),hAPP(v_Q_H,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f1337,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f1000,f1335]) ).

fof(f1335,plain,
    ( spl0_61
  <=> ! [X66,X67] :
        ( ~ class_HOL_Oord(X67)
        | class_HOL_Oord(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f1000,axiom,
    ! [X66,X67] :
      ( ~ class_HOL_Oord(X67)
      | class_HOL_Oord(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f1333,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f999,f1331]) ).

fof(f1331,plain,
    ( spl0_60
  <=> ! [X66,X67] :
        ( ~ class_HOL_Ominus(X67)
        | class_HOL_Ominus(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f999,axiom,
    ! [X66,X67] :
      ( ~ class_HOL_Ominus(X67)
      | class_HOL_Ominus(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f1329,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f998,f1327]) ).

fof(f1327,plain,
    ( spl0_59
  <=> ! [X66,X67] :
        ( ~ class_HOL_Ouminus(X67)
        | class_HOL_Ouminus(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f998,axiom,
    ! [X66,X67] :
      ( ~ class_HOL_Ouminus(X67)
      | class_HOL_Ouminus(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).

fof(f1325,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f997,f1323]) ).

fof(f1323,plain,
    ( spl0_58
  <=> ! [X66,X67] :
        ( ~ class_Orderings_Obot(X67)
        | class_Orderings_Obot(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f997,axiom,
    ! [X66,X67] :
      ( ~ class_Orderings_Obot(X67)
      | class_Orderings_Obot(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f1321,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f996,f1319]) ).

fof(f1319,plain,
    ( spl0_57
  <=> ! [X66,X67] :
        ( ~ class_Orderings_Otop(X67)
        | class_Orderings_Otop(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f996,axiom,
    ! [X66,X67] :
      ( ~ class_Orderings_Otop(X67)
      | class_Orderings_Otop(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

fof(f1317,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f995,f1315]) ).

fof(f1315,plain,
    ( spl0_56
  <=> ! [X66,X67] :
        ( ~ class_Orderings_Oorder(X67)
        | class_Orderings_Oorder(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f995,axiom,
    ! [X66,X67] :
      ( ~ class_Orderings_Oorder(X67)
      | class_Orderings_Oorder(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f1313,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f994,f1311]) ).

fof(f1311,plain,
    ( spl0_55
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Olattice(X67)
        | class_Lattices_Olattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f994,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Olattice(X67)
      | class_Lattices_Olattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f1309,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f993,f1307]) ).

fof(f1307,plain,
    ( spl0_54
  <=> ! [X66,X67] :
        ( ~ class_Orderings_Opreorder(X67)
        | class_Orderings_Opreorder(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f993,axiom,
    ! [X66,X67] :
      ( ~ class_Orderings_Opreorder(X67)
      | class_Orderings_Opreorder(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f1305,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f991,f1303]) ).

fof(f1303,plain,
    ( spl0_53
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Oboolean__algebra(X67)
        | class_Lattices_Oboolean__algebra(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f991,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Oboolean__algebra(X67)
      | class_Lattices_Oboolean__algebra(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

fof(f1301,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f990,f1299]) ).

fof(f1299,plain,
    ( spl0_52
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Obounded__lattice(X67)
        | class_Lattices_Obounded__lattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f990,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Obounded__lattice(X67)
      | class_Lattices_Obounded__lattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f1297,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f989,f1295]) ).

fof(f1295,plain,
    ( spl0_51
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Odistrib__lattice(X67)
        | class_Lattices_Odistrib__lattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f989,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Odistrib__lattice(X67)
      | class_Lattices_Odistrib__lattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f1293,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f988,f1291]) ).

fof(f1291,plain,
    ( spl0_50
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Olattice(X67)
        | class_Lattices_Olower__semilattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f988,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Olattice(X67)
      | class_Lattices_Olower__semilattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f1289,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f987,f1287]) ).

fof(f1287,plain,
    ( spl0_49
  <=> ! [X66,X67] :
        ( ~ class_Lattices_Olattice(X67)
        | class_Lattices_Oupper__semilattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f987,axiom,
    ! [X66,X67] :
      ( ~ class_Lattices_Olattice(X67)
      | class_Lattices_Oupper__semilattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f1285,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f986,f1283]) ).

fof(f1283,plain,
    ( spl0_48
  <=> ! [X66,X67] :
        ( ~ class_Complete__Lattice_Ocomplete__lattice(X67)
        | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X66,X67)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f986,axiom,
    ! [X66,X67] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X67)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X66,X67)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(f1281,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f946,f1279]) ).

fof(f1279,plain,
    ( spl0_47
  <=> ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f946,axiom,
    ! [X0] : c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

fof(f1277,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f276,f1275]) ).

fof(f1275,plain,
    ( spl0_46
  <=> ! [X0] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f276,axiom,
    ! [X0] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Olower__semilattice__class_Oinf(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__inf_0) ).

fof(f1273,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f164,f1271]) ).

fof(f164,axiom,
    ! [X0] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_OrderedGroup_Oab__semigroup__idem__mult(c_Lattices_Oupper__semilattice__class_Osup(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__sup_0) ).

fof(f1269,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f102,f1267]) ).

fof(f1267,plain,
    ( spl0_44
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f102,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omin(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__min_0) ).

fof(f1265,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f15,f1263]) ).

fof(f1263,plain,
    ( spl0_43
  <=> ! [X0] :
        ( ~ class_Orderings_Olinorder(X0)
        | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f15,axiom,
    ! [X0] :
      ( ~ class_Orderings_Olinorder(X0)
      | c_OrderedGroup_Oab__semigroup__idem__mult(c_Orderings_Oord__class_Omax(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__idem__mult__max_0) ).

fof(f1261,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f974,f1259]) ).

fof(f1259,plain,
    ( spl0_42
  <=> ! [X0,X14] :
        ( ~ class_Finite__Set_Ofinite_Ofinite(X0)
        | c_Finite__Set_Ofinite(X14,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f974,axiom,
    ! [X0,X14] :
      ( ~ class_Finite__Set_Ofinite_Ofinite(X0)
      | c_Finite__Set_Ofinite(X14,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

fof(f1257,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f877,f1255]) ).

fof(f1255,plain,
    ( spl0_41
  <=> ! [X52,X51] : c_Com_Ocom_OSemi(X51,X52) != c_Com_Ocom_OSKIP ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f877,axiom,
    ! [X51,X52] : c_Com_Ocom_OSemi(X51,X52) != c_Com_Ocom_OSKIP,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).

fof(f1253,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f251,f1251]) ).

fof(f1251,plain,
    ( spl0_40
  <=> ! [X21] : c_Suc(X21) != X21 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f251,axiom,
    ! [X21] : c_Suc(X21) != X21,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

fof(f1249,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f1037,f1246]) ).

fof(f1246,plain,
    ( spl0_39
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1037,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f1244,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f1036,f1241]) ).

fof(f1241,plain,
    ( spl0_38
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1036,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f1239,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f1035,f1236]) ).

fof(f1236,plain,
    ( spl0_37
  <=> class_HOL_Ouminus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1035,axiom,
    class_HOL_Ouminus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).

fof(f1234,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f1034,f1231]) ).

fof(f1231,plain,
    ( spl0_36
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f1034,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f1229,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f1033,f1226]) ).

fof(f1226,plain,
    ( spl0_35
  <=> class_Orderings_Otop(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f1033,axiom,
    class_Orderings_Otop(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

fof(f1224,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f1032,f1221]) ).

fof(f1221,plain,
    ( spl0_34
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f1032,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f1219,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f1031,f1216]) ).

fof(f1216,plain,
    ( spl0_33
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f1031,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f1214,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f1030,f1211]) ).

fof(f1211,plain,
    ( spl0_32
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f1030,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f1209,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f1029,f1206]) ).

fof(f1206,plain,
    ( spl0_31
  <=> class_Finite__Set_Ofinite_Ofinite(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f1029,axiom,
    class_Finite__Set_Ofinite_Ofinite(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

fof(f1204,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f1028,f1201]) ).

fof(f1201,plain,
    ( spl0_30
  <=> class_Lattices_Oboolean__algebra(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f1028,axiom,
    class_Lattices_Oboolean__algebra(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

fof(f1199,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f1027,f1196]) ).

fof(f1196,plain,
    ( spl0_29
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f1027,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f1194,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f1026,f1191]) ).

fof(f1191,plain,
    ( spl0_28
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f1026,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f1189,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f1025,f1186]) ).

fof(f1186,plain,
    ( spl0_27
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f1025,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f1184,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f1024,f1181]) ).

fof(f1024,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f1179,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f1023,f1176]) ).

fof(f1176,plain,
    ( spl0_25
  <=> class_Complete__Lattice_Ocomplete__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f1023,axiom,
    class_Complete__Lattice_Ocomplete__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

fof(f1174,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f1022,f1171]) ).

fof(f1171,plain,
    ( spl0_24
  <=> class_HOL_Oord(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f1022,axiom,
    class_HOL_Oord(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

fof(f1169,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f1021,f1166]) ).

fof(f1166,plain,
    ( spl0_23
  <=> class_HOL_Ominus(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f1021,axiom,
    class_HOL_Ominus(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).

fof(f1164,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f1020,f1161]) ).

fof(f1161,plain,
    ( spl0_22
  <=> class_Orderings_Obot(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f1020,axiom,
    class_Orderings_Obot(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

fof(f1159,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f1019,f1156]) ).

fof(f1156,plain,
    ( spl0_21
  <=> class_Orderings_Oorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f1019,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

fof(f1154,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f1018,f1151]) ).

fof(f1151,plain,
    ( spl0_20
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f1018,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f1149,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f1017,f1146]) ).

fof(f1017,axiom,
    class_Orderings_Olinorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

fof(f1144,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f1016,f1141]) ).

fof(f1141,plain,
    ( spl0_18
  <=> class_Orderings_Opreorder(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1016,axiom,
    class_Orderings_Opreorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

fof(f1139,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f1015,f1136]) ).

fof(f1136,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1015,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f1134,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f1014,f1131]) ).

fof(f1131,plain,
    ( spl0_16
  <=> class_Lattices_Odistrib__lattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f1014,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

fof(f1129,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f1013,f1126]) ).

fof(f1126,plain,
    ( spl0_15
  <=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f1013,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

fof(f1124,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f1012,f1121]) ).

fof(f1121,plain,
    ( spl0_14
  <=> class_Lattices_Olower__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f1012,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

fof(f1119,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f1011,f1116]) ).

fof(f1011,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

fof(f1114,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f1010,f1111]) ).

fof(f1111,plain,
    ( spl0_12
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f1010,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f1109,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f1009,f1106]) ).

fof(f1106,plain,
    ( spl0_11
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f1009,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f1104,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1008,f1101]) ).

fof(f1101,plain,
    ( spl0_10
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f1008,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f1099,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1007,f1096]) ).

fof(f1096,plain,
    ( spl0_9
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f1007,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f1094,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f1006,f1091]) ).

fof(f1091,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f1006,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1089,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f1005,f1086]) ).

fof(f1086,plain,
    ( spl0_7
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1005,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1084,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f1004,f1081]) ).

fof(f1081,plain,
    ( spl0_6
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f1004,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1079,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f1003,f1076]) ).

fof(f1076,plain,
    ( spl0_5
  <=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1003,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

fof(f1074,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f1002,f1071]) ).

fof(f1071,plain,
    ( spl0_4
  <=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f1002,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

fof(f1069,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f1001,f1066]) ).

fof(f1066,plain,
    ( spl0_3
  <=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1001,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

fof(f1064,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f980,f1061]) ).

fof(f980,axiom,
    ~ hBOOL(c_in(v_x,v_F,t_a)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1059,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f979,f1056]) ).

fof(f1056,plain,
    ( spl0_1
  <=> c_Finite__Set_Ofinite(v_F,t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f979,axiom,
    c_Finite__Set_Ofinite(v_F,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV844-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 21:06:38 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (1903)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43  % (1907)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.44  % (1906)WARNING: value z3 for option sas not known
% 0.21/0.44  % (1904)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.44  % (1906)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.44  % (1905)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.44  % (1908)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.44  % (1910)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.44  % (1909)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.51  % (1908)First to succeed.
% 0.21/0.51  % (1908)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1903"
% 0.21/0.51  % (1908)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Unsatisfiable for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (1908)------------------------------
% 0.21/0.52  % (1908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.52  % (1908)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (1908)Memory used [KB]: 2301
% 0.21/0.52  % (1908)Time elapsed: 0.075 s
% 0.21/0.52  % (1908)Instructions burned: 131 (million)
% 0.21/0.52  % (1903)Success in time 0.161 s
%------------------------------------------------------------------------------