TSTP Solution File: SCT004-1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SCT004-1 : 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 : n004.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 09:00:21 EDT 2024

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :  312
% Syntax   : Number of formulae    :  523 ( 210 unt;   0 def)
%            Number of atoms       :  994 ( 124 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  774 ( 303   ~; 309   |;   0   &)
%                                         ( 162 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :  188 ( 186 usr; 163 prp; 0-3 aty)
%            Number of functors    :   31 (  31 usr;   6 con; 0-5 aty)
%            Number of variables   :  705 ( 705   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1796,plain,
    $false,
    inference(avatar_sat_refutation,[],[f828,f833,f838,f843,f848,f853,f858,f863,f868,f873,f878,f882,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f939,f943,f947,f951,f955,f959,f963,f967,f971,f975,f979,f988,f993,f997,f1001,f1005,f1009,f1013,f1017,f1021,f1025,f1029,f1034,f1038,f1042,f1046,f1051,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1088,f1092,f1096,f1100,f1106,f1112,f1122,f1126,f1130,f1134,f1138,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1190,f1194,f1198,f1202,f1206,f1210,f1214,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1246,f1302,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1351,f1375,f1380,f1384,f1389,f1393,f1397,f1401,f1405,f1409,f1413,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1458,f1462,f1466,f1470,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1502,f1507,f1560,f1564,f1568,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1601,f1605,f1609,f1613,f1617,f1755,f1770,f1774,f1778,f1782,f1783,f1791,f1795]) ).

fof(f1795,plain,
    ( ~ spl0_20
    | ~ spl0_37 ),
    inference(avatar_contradiction_clause,[],[f1792]) ).

fof(f1792,plain,
    ( $false
    | ~ spl0_20
    | ~ spl0_37 ),
    inference(resolution,[],[f983,f914]) ).

fof(f914,plain,
    ( ! [X57] : ~ hBOOL(c_in(c_Pair(X57,X57,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f913]) ).

fof(f913,plain,
    ( spl0_20
  <=> ! [X57] : ~ hBOOL(c_in(c_Pair(X57,X57,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f983,plain,
    ( hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f981]) ).

fof(f981,plain,
    ( spl0_37
  <=> hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f1791,plain,
    ( ~ spl0_13
    | ~ spl0_20 ),
    inference(avatar_contradiction_clause,[],[f1788]) ).

fof(f1788,plain,
    ( $false
    | ~ spl0_13
    | ~ spl0_20 ),
    inference(resolution,[],[f886,f914]) ).

fof(f886,plain,
    ( hBOOL(c_in(c_Pair(v_xa,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f884]) ).

fof(f884,plain,
    ( spl0_13
  <=> hBOOL(c_in(c_Pair(v_xa,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f1783,plain,
    ( spl0_14
    | spl0_39
    | spl0_38
    | ~ spl0_158 ),
    inference(avatar_split_clause,[],[f1757,f1753,f985,f990,f888]) ).

fof(f888,plain,
    ( spl0_14
  <=> v_x = v_xa ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f990,plain,
    ( spl0_39
  <=> hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f985,plain,
    ( spl0_38
  <=> hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f1753,plain,
    ( spl0_158
  <=> ! [X62,X63] :
        ( X62 = X63
        | hBOOL(c_in(c_Pair(X62,X63,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X63,X62,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1757,plain,
    ( hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | v_x = v_xa
    | spl0_38
    | ~ spl0_158 ),
    inference(resolution,[],[f1754,f987]) ).

fof(f987,plain,
    ( ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_38 ),
    inference(avatar_component_clause,[],[f985]) ).

fof(f1754,plain,
    ( ! [X62,X63] :
        ( hBOOL(c_in(c_Pair(X63,X62,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | hBOOL(c_in(c_Pair(X62,X63,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
        | X62 = X63 )
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1753]) ).

fof(f1782,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f130,f1780]) ).

fof(f1780,plain,
    ( spl0_162
  <=> ! [X2,X21,X4] :
        ( ~ class_Orderings_Oorder(X2)
        | X4 = X21
        | ~ c_lessequals(X21,X4,X2)
        | ~ c_lessequals(X4,X21,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f130,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Orderings_Oorder(X2)
      | X4 = X21
      | ~ c_lessequals(X21,X4,X2)
      | ~ c_lessequals(X4,X21,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

fof(f1778,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f98,f1776]) ).

fof(f1776,plain,
    ( spl0_161
  <=> ! [X2,X4,X3,X1] :
        ( ~ hBOOL(hAPP(X1,X4))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f98,axiom,
    ! [X2,X3,X1,X4] :
      ( ~ hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

fof(f1774,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f97,f1772]) ).

fof(f1772,plain,
    ( spl0_160
  <=> ! [X4,X2,X1,X3] :
        ( ~ hBOOL(hAPP(X3,X4))
        | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).

fof(f97,axiom,
    ! [X2,X3,X1,X4] :
      ( ~ hBOOL(hAPP(X3,X4))
      | hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

fof(f1770,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f74,f1768]) ).

fof(f1768,plain,
    ( spl0_159
  <=> ! [X2,X1,X3] : c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).

fof(f74,axiom,
    ! [X2,X3,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(X3,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

fof(f1755,plain,
    ( spl0_158
    | spl0_158 ),
    inference(avatar_split_clause,[],[f675,f1753,f1753]) ).

fof(f675,axiom,
    ! [X21,X62,X63,X32] :
      ( X21 = X32
      | X62 = X63
      | hBOOL(c_in(c_Pair(X32,X21,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X21,X32,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X63,X62,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | hBOOL(c_in(c_Pair(X62,X63,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_17) ).

fof(f1617,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f550,f1615]) ).

fof(f1615,plain,
    ( spl0_157
  <=> ! [X2,X15] : c_Transitive__Closure_Otrancl(X15,X2) = c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X2),X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f550,axiom,
    ! [X2,X15] : c_Transitive__Closure_Otrancl(X15,X2) = c_Relation_Orel__comp(X15,c_Transitive__Closure_Ortrancl(X15,X2),X2,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).

fof(f1613,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f549,f1611]) ).

fof(f1611,plain,
    ( spl0_156
  <=> ! [X2,X15] : c_Transitive__Closure_Otrancl(X15,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X2),X15,X2,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f549,axiom,
    ! [X2,X15] : c_Transitive__Closure_Otrancl(X15,X2) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X15,X2),X15,X2,X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).

fof(f1609,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f414,f1607]) ).

fof(f1607,plain,
    ( spl0_155
  <=> ! [X2,X15] :
        ( c_Wellfounded_Owf(X15,X2)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X15,X2),c_Wellfounded_Oacc(X15,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f414,axiom,
    ! [X2,X15] :
      ( c_Wellfounded_Owf(X15,X2)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1(X15,X2),c_Wellfounded_Oacc(X15,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).

fof(f1605,plain,
    ( spl0_154
    | ~ spl0_5
    | ~ spl0_77 ),
    inference(avatar_split_clause,[],[f1257,f1157,f845,f1603]) ).

fof(f1603,plain,
    ( spl0_154
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f845,plain,
    ( spl0_5
  <=> class_Lattices_Obounded__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f1157,plain,
    ( spl0_77
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X4,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f1257,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_bool),X0,tc_bool) = X0
    | ~ spl0_5
    | ~ spl0_77 ),
    inference(resolution,[],[f1158,f847]) ).

fof(f847,plain,
    ( class_Lattices_Obounded__lattice(tc_bool)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f845]) ).

fof(f1158,plain,
    ( ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X4,X2) = X4 )
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1157]) ).

fof(f1601,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f413,f1599]) ).

fof(f1599,plain,
    ( spl0_153
  <=> ! [X2,X15] :
        ( c_Wellfounded_Owf(X15,X2)
        | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X15,X2),c_Wellfounded_Oacc(X15,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f413,axiom,
    ! [X2,X15] :
      ( c_Wellfounded_Owf(X15,X2)
      | ~ hBOOL(c_in(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1(X15,X2),c_Wellfounded_Oacc(X15,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).

fof(f1596,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f354,f1594]) ).

fof(f1594,plain,
    ( spl0_152
  <=> ! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f354,axiom,
    ! [X2] : c_Relation_Orefl__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).

fof(f1592,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f135,f1590]) ).

fof(f1590,plain,
    ( spl0_151
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X4,X21,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = X21 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f135,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X4,X21,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

fof(f1588,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f134,f1586]) ).

fof(f1586,plain,
    ( spl0_150
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X4,X21,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) != X21 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f134,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X4,X21,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) != X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

fof(f1584,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f133,f1582]) ).

fof(f1582,plain,
    ( spl0_149
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | ~ c_lessequals(X21,X4,X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f133,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | ~ c_lessequals(X21,X4,X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

fof(f1580,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f76,f1578]) ).

fof(f1578,plain,
    ( spl0_148
  <=> ! [X2,X1,X4] : c_Set_Oinsert(X4,X1,X2) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f76,axiom,
    ! [X2,X1,X4] : c_Set_Oinsert(X4,X1,X2) = c_Set_Oinsert(X4,c_Set_Oinsert(X4,X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

fof(f1576,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f62,f1574]) ).

fof(f1574,plain,
    ( spl0_147
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X21,X4,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = X21 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f62,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X21,X4,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = X21 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

fof(f1572,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f61,f1570]) ).

fof(f1570,plain,
    ( spl0_146
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(X4,X21,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) != X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f61,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(X4,X21,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) != X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

fof(f1568,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f60,f1566]) ).

fof(f1566,plain,
    ( spl0_145
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | ~ c_lessequals(X4,X21,X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f60,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | ~ c_lessequals(X4,X21,X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

fof(f1564,plain,
    ( spl0_144
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(avatar_split_clause,[],[f1255,f1153,f845,f1562]) ).

fof(f1562,plain,
    ( spl0_144
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f1153,plain,
    ( spl0_76
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X2),X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f1255,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) = X0
    | ~ spl0_5
    | ~ spl0_76 ),
    inference(resolution,[],[f1154,f847]) ).

fof(f1154,plain,
    ( ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X2),X2) = X4 )
    | ~ spl0_76 ),
    inference(avatar_component_clause,[],[f1153]) ).

fof(f1560,plain,
    ( spl0_143
    | ~ spl0_141 ),
    inference(avatar_split_clause,[],[f1503,f1500,f1558]) ).

fof(f1558,plain,
    ( spl0_143
  <=> ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f1500,plain,
    ( spl0_141
  <=> ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f1503,plain,
    ( ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2,X2)
    | ~ spl0_141 ),
    inference(forward_demodulation,[],[f1501,f365]) ).

fof(f365,axiom,
    ! [X2] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)) = c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).

fof(f1501,plain,
    ( ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2)
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1500]) ).

fof(f1507,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f706,f1505]) ).

fof(f1505,plain,
    ( spl0_142
  <=> ! [X2,X1] : c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f706,plain,
    ! [X2,X1] : c_Relation_ODomain(c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),X2,X2) = X1,
    inference(definition_unfolding,[],[f532,f548]) ).

fof(f548,axiom,
    ! [X2,X7,X15] : c_Relation_ORange(X15,X7,X2) = c_Relation_ODomain(c_Relation_Oconverse(X15,X7,X2),X2,X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).

fof(f532,axiom,
    ! [X2,X1] : c_Relation_ORange(c_Relation_OId__on(X1,X2),X2,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).

fof(f1502,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f704,f1500]) ).

fof(f704,plain,
    ! [X2] : c_Relation_Osingle__valued(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2,X2),
    inference(definition_unfolding,[],[f507,f363]) ).

fof(f363,axiom,
    ! [X2] : c_Relation_OId(X2) = c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).

fof(f507,axiom,
    ! [X2] : c_Relation_Osingle__valued(c_Relation_OId(X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).

fof(f1498,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f554,f1496]) ).

fof(f1496,plain,
    ( spl0_140
  <=> ! [X2,X1,X15] :
        ( ~ c_Relation_Ototal__on(X1,X15,X2)
        | c_Relation_Ototal__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f554,axiom,
    ! [X2,X1,X15] :
      ( ~ c_Relation_Ototal__on(X1,X15,X2)
      | c_Relation_Ototal__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).

fof(f1494,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f553,f1492]) ).

fof(f1492,plain,
    ( spl0_139
  <=> ! [X2,X1,X15] :
        ( c_Relation_Ototal__on(X1,X15,X2)
        | ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f553,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Ototal__on(X1,X15,X2)
      | ~ c_Relation_Ototal__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).

fof(f1490,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f517,f1488]) ).

fof(f1488,plain,
    ( spl0_138
  <=> ! [X7] :
        ( ~ class_Orderings_Obot(X7)
        | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f517,axiom,
    ! [X7] :
      ( ~ class_Orderings_Obot(X7)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,X7)),v_x) = c_Orderings_Obot__class_Obot(X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).

fof(f1486,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f504,f1484]) ).

fof(f1484,plain,
    ( spl0_137
  <=> ! [X2,X5] :
        ( c_Wellfounded_Owf(X5,X2)
        | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X5,X5,X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f504,axiom,
    ! [X2,X5] :
      ( c_Wellfounded_Owf(X5,X2)
      | ~ c_Wellfounded_Owf(c_Relation_Orel__comp(X5,X5,X2,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).

fof(f1482,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f503,f1480]) ).

fof(f1480,plain,
    ( spl0_136
  <=> ! [X2,X5] :
        ( ~ c_Wellfounded_Owf(X5,X2)
        | c_Wellfounded_Owf(c_Relation_Orel__comp(X5,X5,X2,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f503,axiom,
    ! [X2,X5] :
      ( ~ c_Wellfounded_Owf(X5,X2)
      | c_Wellfounded_Owf(c_Relation_Orel__comp(X5,X5,X2,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).

fof(f1478,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f501,f1476]) ).

fof(f1476,plain,
    ( spl0_135
  <=> ! [X2,X1,X15] :
        ( ~ c_Relation_Orefl__on(X1,X15,X2)
        | c_Relation_Orefl__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f501,axiom,
    ! [X2,X1,X15] :
      ( ~ c_Relation_Orefl__on(X1,X15,X2)
      | c_Relation_Orefl__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).

fof(f1474,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f500,f1472]) ).

fof(f1472,plain,
    ( spl0_134
  <=> ! [X2,X1,X15] :
        ( c_Relation_Orefl__on(X1,X15,X2)
        | ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f500,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Orefl__on(X1,X15,X2)
      | ~ c_Relation_Orefl__on(X1,c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).

fof(f1470,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f490,f1468]) ).

fof(f1468,plain,
    ( spl0_133
  <=> ! [X2,X15] : c_Relation_ODomain(X15,X2,X2) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X15,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f490,axiom,
    ! [X2,X15] : c_Relation_ODomain(X15,X2,X2) = c_Relation_ODomain(c_Transitive__Closure_Otrancl(X15,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).

fof(f1466,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f270,f1464]) ).

fof(f1464,plain,
    ( spl0_132
  <=> ! [X0,X16,X2,X7] : hAPP(c_snd(X7,X2),c_Pair(X0,X16,X7,X2)) = X16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f270,axiom,
    ! [X2,X0,X7,X16] : hAPP(c_snd(X7,X2),c_Pair(X0,X16,X7,X2)) = X16,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_snd__conv_0) ).

fof(f1462,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f268,f1460]) ).

fof(f1460,plain,
    ( spl0_131
  <=> ! [X0,X16,X2,X7] : hAPP(c_fst(X2,X7),c_Pair(X0,X16,X2,X7)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f268,axiom,
    ! [X2,X0,X7,X16] : hAPP(c_fst(X2,X7),c_Pair(X0,X16,X2,X7)) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fst__conv_0) ).

fof(f1458,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f267,f1456]) ).

fof(f1456,plain,
    ( spl0_130
  <=> ! [X2,X0,X1] :
        ( ~ hBOOL(c_in(X0,X1,X2))
        | c_Set_Oinsert(X0,X1,X2) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f267,axiom,
    ! [X2,X0,X1] :
      ( ~ hBOOL(c_in(X0,X1,X2))
      | c_Set_Oinsert(X0,X1,X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

fof(f1454,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f221,f1452]) ).

fof(f1452,plain,
    ( spl0_129
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = c_Lattices_Oupper__semilattice__class_Osup(X21,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f221,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = c_Lattices_Oupper__semilattice__class_Osup(X21,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f1450,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f220,f1448]) ).

fof(f1448,plain,
    ( spl0_128
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = c_Lattices_Oupper__semilattice__class_Osup(X21,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f220,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2) = c_Lattices_Oupper__semilattice__class_Osup(X21,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f1446,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f190,f1444]) ).

fof(f1444,plain,
    ( spl0_127
  <=> ! [X4,X21,X1,X2] :
        ( ~ hBOOL(hAPP(X1,X4))
        | hBOOL(hAPP(c_Set_Oinsert(X21,X1,X2),X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f190,axiom,
    ! [X2,X21,X1,X4] :
      ( ~ hBOOL(hAPP(X1,X4))
      | hBOOL(hAPP(c_Set_Oinsert(X21,X1,X2),X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

fof(f1442,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f181,f1440]) ).

fof(f1440,plain,
    ( spl0_126
  <=> ! [X2,X1,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f181,axiom,
    ! [X2,X3,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

fof(f1438,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f176,f1436]) ).

fof(f1436,plain,
    ( spl0_125
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = c_Lattices_Olower__semilattice__class_Oinf(X21,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f176,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = c_Lattices_Olower__semilattice__class_Oinf(X21,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f1434,plain,
    spl0_124,
    inference(avatar_split_clause,[],[f163,f1432]) ).

fof(f1432,plain,
    ( spl0_124
  <=> ! [X2,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f163,axiom,
    ! [X2,X3,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

fof(f1430,plain,
    spl0_123,
    inference(avatar_split_clause,[],[f162,f1428]) ).

fof(f1428,plain,
    ( spl0_123
  <=> ! [X2,X1,X3] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f162,axiom,
    ! [X2,X3,X1] : c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X1,X3,tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

fof(f1426,plain,
    spl0_122,
    inference(avatar_split_clause,[],[f131,f1424]) ).

fof(f1424,plain,
    ( spl0_122
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f131,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f1422,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f119,f1420]) ).

fof(f1420,plain,
    ( spl0_121
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f119,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f1418,plain,
    ( ~ spl0_120
    | spl0_39
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1307,f1240,f990,f1415]) ).

fof(f1415,plain,
    ( spl0_120
  <=> hBOOL(hAPP(v_L,c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f1240,plain,
    ( spl0_97
  <=> ! [X4,X9,X2] :
        ( ~ hBOOL(hAPP(X9,X4))
        | hBOOL(c_in(X4,X9,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f1307,plain,
    ( ~ hBOOL(hAPP(v_L,c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_39
    | ~ spl0_97 ),
    inference(resolution,[],[f1241,f992]) ).

fof(f992,plain,
    ( ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_39 ),
    inference(avatar_component_clause,[],[f990]) ).

fof(f1241,plain,
    ( ! [X2,X9,X4] :
        ( hBOOL(c_in(X4,X9,X2))
        | ~ hBOOL(hAPP(X9,X4)) )
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1240]) ).

fof(f1413,plain,
    spl0_119,
    inference(avatar_split_clause,[],[f110,f1411]) ).

fof(f1411,plain,
    ( spl0_119
  <=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f110,axiom,
    ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

fof(f1409,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f109,f1407]) ).

fof(f1407,plain,
    ( spl0_118
  <=> ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f109,axiom,
    ! [X2,X3] : c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X3,tc_fun(X2,tc_bool)) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

fof(f1405,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f93,f1403]) ).

fof(f1403,plain,
    ( spl0_117
  <=> ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f93,axiom,
    ! [X2,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

fof(f1401,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f92,f1399]) ).

fof(f1399,plain,
    ( spl0_116
  <=> ! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f92,axiom,
    ! [X2,X1] : c_HOL_Ominus__class_Ominus(X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

fof(f1397,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f75,f1395]) ).

fof(f1395,plain,
    ( spl0_115
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = c_Lattices_Olower__semilattice__class_Oinf(X21,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f75,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2) = c_Lattices_Olower__semilattice__class_Oinf(X21,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f1393,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f65,f1391]) ).

fof(f1391,plain,
    ( spl0_114
  <=> ! [X2,X1,X3] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f65,axiom,
    ! [X2,X3,X1] : c_lessequals(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).

fof(f1389,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f64,f1387]) ).

fof(f1387,plain,
    ( spl0_113
  <=> ! [X2,X1,X3] : c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f64,axiom,
    ! [X2,X3,X1] : c_lessequals(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,tc_fun(X2,tc_bool)),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).

fof(f1384,plain,
    ( spl0_112
    | ~ spl0_109 ),
    inference(avatar_split_clause,[],[f1352,f1349,f1382]) ).

fof(f1382,plain,
    ( spl0_112
  <=> ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f1349,plain,
    ( spl0_109
  <=> ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f1352,plain,
    ( ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2)
    | ~ spl0_109 ),
    inference(forward_demodulation,[],[f1350,f365]) ).

fof(f1350,plain,
    ( ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
    | ~ spl0_109 ),
    inference(avatar_component_clause,[],[f1349]) ).

fof(f1380,plain,
    ( ~ spl0_111
    | spl0_38
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1306,f1240,f985,f1377]) ).

fof(f1377,plain,
    ( spl0_111
  <=> hBOOL(hAPP(v_L,c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f1306,plain,
    ( ~ hBOOL(hAPP(v_L,c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | spl0_38
    | ~ spl0_97 ),
    inference(resolution,[],[f1241,f987]) ).

fof(f1375,plain,
    ( spl0_110
    | ~ spl0_108 ),
    inference(avatar_split_clause,[],[f1347,f1344,f1373]) ).

fof(f1373,plain,
    ( spl0_110
  <=> ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1344,plain,
    ( spl0_108
  <=> ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f1347,plain,
    ( ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2),X2)
    | ~ spl0_108 ),
    inference(forward_demodulation,[],[f1345,f365]) ).

fof(f1345,plain,
    ( ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2)
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1344]) ).

fof(f1351,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f702,f1349]) ).

fof(f702,plain,
    ! [X2] : c_Relation_Osym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2),
    inference(definition_unfolding,[],[f494,f363]) ).

fof(f494,axiom,
    ! [X2] : c_Relation_Osym(c_Relation_OId(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).

fof(f1346,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f701,f1344]) ).

fof(f701,plain,
    ! [X2] : c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),X2),
    inference(definition_unfolding,[],[f529,f363]) ).

fof(f529,axiom,
    ! [X2] : c_Relation_Oantisym(c_Relation_OId(X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).

fof(f1342,plain,
    ( spl0_107
    | ~ spl0_20
    | ~ spl0_97 ),
    inference(avatar_split_clause,[],[f1305,f1240,f913,f1340]) ).

fof(f1340,plain,
    ( spl0_107
  <=> ! [X0] : ~ hBOOL(hAPP(v_L,c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f1305,plain,
    ( ! [X0] : ~ hBOOL(hAPP(v_L,c_Pair(X0,X0,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ spl0_20
    | ~ spl0_97 ),
    inference(resolution,[],[f1241,f914]) ).

fof(f1338,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f527,f1336]) ).

fof(f1336,plain,
    ( spl0_106
  <=> ! [X2,X1] : c_Relation_OId__on(X1,X2) = c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f527,axiom,
    ! [X2,X1] : c_Relation_OId__on(X1,X2) = c_Relation_Oconverse(c_Relation_OId__on(X1,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).

fof(f1334,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f518,f1332]) ).

fof(f1332,plain,
    ( spl0_105
  <=> ! [X15,X19,X7,X2] :
        ( ~ c_Relation_Osym(X15,X2)
        | c_Relation_Osym(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f518,axiom,
    ! [X2,X19,X7,X15] :
      ( ~ c_Relation_Osym(X15,X2)
      | c_Relation_Osym(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).

fof(f1330,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f515,f1328]) ).

fof(f1328,plain,
    ( spl0_104
  <=> ! [X15,X19,X7,X2] :
        ( ~ c_Wellfounded_Owf(X15,X2)
        | c_Wellfounded_Owf(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f515,axiom,
    ! [X2,X19,X7,X15] :
      ( ~ c_Wellfounded_Owf(X15,X2)
      | c_Wellfounded_Owf(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).

fof(f1326,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f481,f1324]) ).

fof(f1324,plain,
    ( spl0_103
  <=> ! [X2,X4,X15] :
        ( ~ c_Wellfounded_Owf(X15,X2)
        | hBOOL(c_in(X4,c_Wellfounded_Oacc(X15,X2),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f481,axiom,
    ! [X2,X4,X15] :
      ( ~ c_Wellfounded_Owf(X15,X2)
      | hBOOL(c_in(X4,c_Wellfounded_Oacc(X15,X2),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).

fof(f1322,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f382,f1320]) ).

fof(f1320,plain,
    ( spl0_102
  <=> ! [X15,X19,X7,X2] :
        ( ~ c_Relation_Otrans(X15,X2)
        | c_Relation_Otrans(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f382,axiom,
    ! [X2,X19,X7,X15] :
      ( ~ c_Relation_Otrans(X15,X2)
      | c_Relation_Otrans(c_Relation_Oinv__image(X15,X19,X2,X7),X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).

fof(f1318,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f83,f1316]) ).

fof(f1316,plain,
    ( spl0_101
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f83,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(c_Orderings_Obot__class_Obot(X2),X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

fof(f1314,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f82,f1312]) ).

fof(f1312,plain,
    ( spl0_100
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Obounded__lattice(X2)
        | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f82,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Orderings_Obot__class_Obot(X2) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Orderings_Obot__class_Obot(X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

fof(f1302,plain,
    ( ~ spl0_7
    | spl0_99
    | ~ spl0_67
    | ~ spl0_74 ),
    inference(avatar_split_clause,[],[f1251,f1145,f1110,f1300,f855]) ).

fof(f855,plain,
    ( spl0_7
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f1300,plain,
    ( spl0_99
  <=> ! [X0] : c_lessequals(X0,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f1110,plain,
    ( spl0_67
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f1145,plain,
    ( spl0_74
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f1251,plain,
    ( ! [X0] :
        ( c_lessequals(X0,X0,tc_bool)
        | ~ class_Lattices_Olattice(tc_bool) )
    | ~ spl0_67
    | ~ spl0_74 ),
    inference(superposition,[],[f1146,f1111]) ).

fof(f1111,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1110]) ).

fof(f1146,plain,
    ( ! [X2,X21,X4] :
        ( c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2)
        | ~ class_Lattices_Olattice(X2) )
    | ~ spl0_74 ),
    inference(avatar_component_clause,[],[f1145]) ).

fof(f1246,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f657,f1244]) ).

fof(f1244,plain,
    ( spl0_98
  <=> ! [X4,X9,X2] :
        ( hBOOL(hAPP(X9,X4))
        | ~ hBOOL(c_in(X4,X9,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f657,axiom,
    ! [X2,X9,X4] :
      ( hBOOL(hAPP(X9,X4))
      | ~ hBOOL(c_in(X4,X9,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

fof(f1242,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f656,f1240]) ).

fof(f656,axiom,
    ! [X2,X9,X4] :
      ( ~ hBOOL(hAPP(X9,X4))
      | hBOOL(c_in(X4,X9,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

fof(f1238,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f559,f1236]) ).

fof(f1236,plain,
    ( spl0_96
  <=> ! [X2,X15] :
        ( c_Relation_Otrans(X15,X2)
        | ~ c_Relation_Otrans(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f559,axiom,
    ! [X2,X15] :
      ( c_Relation_Otrans(X15,X2)
      | ~ c_Relation_Otrans(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).

fof(f1234,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f558,f1232]) ).

fof(f1232,plain,
    ( spl0_95
  <=> ! [X2,X15] :
        ( ~ c_Relation_Otrans(X15,X2)
        | c_Relation_Otrans(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f558,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Otrans(X15,X2)
      | c_Relation_Otrans(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).

fof(f1230,plain,
    ( spl0_94
    | ~ spl0_3
    | ~ spl0_56 ),
    inference(avatar_split_clause,[],[f1107,f1062,f835,f1228]) ).

fof(f1228,plain,
    ( spl0_94
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f835,plain,
    ( spl0_3
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f1062,plain,
    ( spl0_56
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f1107,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
    | ~ spl0_3
    | ~ spl0_56 ),
    inference(resolution,[],[f1063,f837]) ).

fof(f837,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f835]) ).

fof(f1063,plain,
    ( ! [X2,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X2) = X4 )
    | ~ spl0_56 ),
    inference(avatar_component_clause,[],[f1062]) ).

fof(f1226,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f557,f1224]) ).

fof(f1224,plain,
    ( spl0_93
  <=> ! [X2,X15] : c_Transitive__Closure_Ortrancl(X15,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X15,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f557,axiom,
    ! [X2,X15] : c_Transitive__Closure_Ortrancl(X15,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X15,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).

fof(f1222,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f556,f1220]) ).

fof(f1220,plain,
    ( spl0_92
  <=> ! [X2,X5] : c_Transitive__Closure_Ortrancl(X5,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X5,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f556,axiom,
    ! [X2,X5] : c_Transitive__Closure_Ortrancl(X5,X2) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Otrancl(X5,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).

fof(f1218,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f538,f1216]) ).

fof(f1216,plain,
    ( spl0_91
  <=> ! [X2,X15] :
        ( ~ c_Relation_Oantisym(X15,X2)
        | c_Relation_Oantisym(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f538,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Oantisym(X15,X2)
      | c_Relation_Oantisym(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).

fof(f1214,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f537,f1212]) ).

fof(f1212,plain,
    ( spl0_90
  <=> ! [X2,X15] :
        ( c_Relation_Oantisym(X15,X2)
        | ~ c_Relation_Oantisym(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f537,axiom,
    ! [X2,X15] :
      ( c_Relation_Oantisym(X15,X2)
      | ~ c_Relation_Oantisym(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).

fof(f1210,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f534,f1208]) ).

fof(f1208,plain,
    ( spl0_89
  <=> ! [X2,X7,X15] : c_Relation_Oconverse(c_Relation_Oconverse(X15,X2,X7),X7,X2) = X15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f534,axiom,
    ! [X2,X7,X15] : c_Relation_Oconverse(c_Relation_Oconverse(X15,X2,X7),X7,X2) = X15,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).

fof(f1206,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f520,f1204]) ).

fof(f1204,plain,
    ( spl0_88
  <=> ! [X2,X5] : c_Transitive__Closure_Ortrancl(X5,X2) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X5,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f520,axiom,
    ! [X2,X5] : c_Transitive__Closure_Ortrancl(X5,X2) = c_Transitive__Closure_Otrancl(c_Transitive__Closure_Ortrancl(X5,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).

fof(f1202,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f510,f1200]) ).

fof(f1200,plain,
    ( spl0_87
  <=> ! [X2,X15] :
        ( c_Relation_Osym(X15,X2)
        | c_Relation_Oconverse(X15,X2,X2) != X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f510,axiom,
    ! [X2,X15] :
      ( c_Relation_Osym(X15,X2)
      | c_Relation_Oconverse(X15,X2,X2) != X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).

fof(f1198,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f509,f1196]) ).

fof(f1196,plain,
    ( spl0_86
  <=> ! [X2,X15] :
        ( ~ c_Relation_Osym(X15,X2)
        | c_Relation_Oconverse(X15,X2,X2) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f509,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Osym(X15,X2)
      | c_Relation_Oconverse(X15,X2,X2) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).

fof(f1194,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f489,f1192]) ).

fof(f1192,plain,
    ( spl0_85
  <=> ! [X2,X15] :
        ( ~ c_Relation_Osym(X15,X2)
        | c_Relation_Osym(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f489,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Osym(X15,X2)
      | c_Relation_Osym(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).

fof(f1190,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f488,f1188]) ).

fof(f1188,plain,
    ( spl0_84
  <=> ! [X2,X15] :
        ( c_Relation_Osym(X15,X2)
        | ~ c_Relation_Osym(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f488,axiom,
    ! [X2,X15] :
      ( c_Relation_Osym(X15,X2)
      | ~ c_Relation_Osym(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).

fof(f1183,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f161,f1181]) ).

fof(f1181,plain,
    ( spl0_83
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f161,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

fof(f1179,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f160,f1177]) ).

fof(f1177,plain,
    ( spl0_82
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olower__semilattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X21,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f160,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X21,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

fof(f1175,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f156,f1173]) ).

fof(f1173,plain,
    ( spl0_81
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X21,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f156,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X21,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

fof(f1171,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f155,f1169]) ).

fof(f1169,plain,
    ( spl0_80
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f155,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(X4,X21,X2),X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

fof(f1167,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f124,f1165]) ).

fof(f1165,plain,
    ( spl0_79
  <=> ! [X2,X15] :
        ( ~ c_Wellfounded_Oacyclic(X15,X2)
        | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f124,axiom,
    ! [X2,X15] :
      ( ~ c_Wellfounded_Oacyclic(X15,X2)
      | c_Wellfounded_Oacyclic(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).

fof(f1163,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f123,f1161]) ).

fof(f1161,plain,
    ( spl0_78
  <=> ! [X2,X15] :
        ( c_Wellfounded_Oacyclic(X15,X2)
        | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X15,X2,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f123,axiom,
    ! [X2,X15] :
      ( c_Wellfounded_Oacyclic(X15,X2)
      | ~ c_Wellfounded_Oacyclic(c_Relation_Oconverse(X15,X2,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).

fof(f1159,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f108,f1157]) ).

fof(f108,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Orderings_Obot__class_Obot(X2),X4,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

fof(f1155,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f107,f1153]) ).

fof(f107,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Obounded__lattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,c_Orderings_Obot__class_Obot(X2),X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

fof(f1151,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f86,f1149]) ).

fof(f1149,plain,
    ( spl0_75
  <=> ! [X2,X0,X3] : c_lessequals(X3,c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f86,axiom,
    ! [X2,X3,X0] : c_lessequals(X3,c_Set_Oinsert(X0,X3,X2),tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

fof(f1147,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f73,f1145]) ).

fof(f73,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

fof(f1143,plain,
    ( spl0_73
    | ~ spl0_1
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f1117,f1098,f825,f1140]) ).

fof(f1140,plain,
    ( spl0_73
  <=> v_L = c_Transitive__Closure_Otrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f825,plain,
    ( spl0_1
  <=> c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f1098,plain,
    ( spl0_65
  <=> ! [X2,X15] :
        ( ~ c_Relation_Otrans(X15,X2)
        | c_Transitive__Closure_Otrancl(X15,X2) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f1117,plain,
    ( v_L = c_Transitive__Closure_Otrancl(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_1
    | ~ spl0_65 ),
    inference(resolution,[],[f1099,f827]) ).

fof(f827,plain,
    ( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f825]) ).

fof(f1099,plain,
    ( ! [X2,X15] :
        ( ~ c_Relation_Otrans(X15,X2)
        | c_Transitive__Closure_Otrancl(X15,X2) = X15 )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f1098]) ).

fof(f1138,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f72,f1136]) ).

fof(f1136,plain,
    ( spl0_72
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Olattice(X2)
        | c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f72,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Olattice(X2)
      | c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

fof(f1134,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f69,f1132]) ).

fof(f1132,plain,
    ( spl0_71
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f69,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X21,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

fof(f1130,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f68,f1128]) ).

fof(f1128,plain,
    ( spl0_70
  <=> ! [X2,X21,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f68,axiom,
    ! [X2,X21,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_lessequals(X4,c_Lattices_Oupper__semilattice__class_Osup(X4,X21,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

fof(f1126,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f7,f1124]) ).

fof(f1124,plain,
    ( spl0_69
  <=> ! [X2,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f7,axiom,
    ! [X2,X1] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

fof(f1122,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f2,f1120]) ).

fof(f1120,plain,
    ( spl0_68
  <=> ! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f2,axiom,
    ! [X2,X0,X1] : c_Set_Oinsert(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

fof(f1112,plain,
    ( spl0_67
    | ~ spl0_2
    | ~ spl0_50 ),
    inference(avatar_split_clause,[],[f1101,f1036,f830,f1110]) ).

fof(f830,plain,
    ( spl0_2
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1036,plain,
    ( spl0_50
  <=> ! [X2,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X2) = X4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f1101,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_2
    | ~ spl0_50 ),
    inference(resolution,[],[f1037,f832]) ).

fof(f832,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f830]) ).

fof(f1037,plain,
    ( ! [X2,X4] :
        ( ~ class_Lattices_Oupper__semilattice(X2)
        | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X2) = X4 )
    | ~ spl0_50 ),
    inference(avatar_component_clause,[],[f1036]) ).

fof(f1106,plain,
    ( spl0_66
    | ~ spl0_53 ),
    inference(avatar_split_clause,[],[f1052,f1049,f1104]) ).

fof(f1104,plain,
    ( spl0_66
  <=> ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1049,plain,
    ( spl0_53
  <=> ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f1052,plain,
    ( ! [X2] : c_Wellfounded_Owf(c_Relation_OId__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2),X2)
    | ~ spl0_53 ),
    inference(forward_demodulation,[],[f1050,f365]) ).

fof(f1050,plain,
    ( ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f1049]) ).

fof(f1100,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f563,f1098]) ).

fof(f563,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Otrans(X15,X2)
      | c_Transitive__Closure_Otrancl(X15,X2) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).

fof(f1096,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f541,f1094]) ).

fof(f1094,plain,
    ( spl0_64
  <=> ! [X2,X1,X15] :
        ( ~ c_Equiv__Relations_Oequiv(X1,X15,X2)
        | c_Relation_Orefl__on(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f541,axiom,
    ! [X2,X1,X15] :
      ( ~ c_Equiv__Relations_Oequiv(X1,X15,X2)
      | c_Relation_Orefl__on(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).

fof(f1092,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f522,f1090]) ).

fof(f1090,plain,
    ( spl0_63
  <=> ! [X2,X15] :
        ( ~ c_Wellfounded_Owf(X15,X2)
        | c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X15,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f522,axiom,
    ! [X2,X15] :
      ( ~ c_Wellfounded_Owf(X15,X2)
      | c_Wellfounded_Owf(c_Transitive__Closure_Otrancl(X15,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).

fof(f1088,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f508,f1086]) ).

fof(f1086,plain,
    ( spl0_62
  <=> ! [X2,X1] : c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f508,axiom,
    ! [X2,X1] : c_Relation_ODomain(c_Relation_OId__on(X1,X2),X2,X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).

fof(f1084,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f502,f1082]) ).

fof(f1082,plain,
    ( spl0_61
  <=> ! [X2,X15] :
        ( ~ c_Relation_Osym(X15,X2)
        | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X15,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f502,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Osym(X15,X2)
      | c_Relation_Osym(c_Transitive__Closure_Ortrancl(X15,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).

fof(f1080,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f484,f1078]) ).

fof(f1078,plain,
    ( spl0_60
  <=> ! [X2,X15] :
        ( ~ c_Relation_Osym(X15,X2)
        | c_Relation_Osym(c_Transitive__Closure_Otrancl(X15,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f484,axiom,
    ! [X2,X15] :
      ( ~ c_Relation_Osym(X15,X2)
      | c_Relation_Osym(c_Transitive__Closure_Otrancl(X15,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).

fof(f1076,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f477,f1074]) ).

fof(f1074,plain,
    ( spl0_59
  <=> ! [X2,X0] : ~ hBOOL(c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f477,axiom,
    ! [X2,X0] : ~ hBOOL(c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

fof(f1072,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f366,f1070]) ).

fof(f1070,plain,
    ( spl0_58
  <=> ! [X2,X15] :
        ( ~ c_Wellfounded_Oacyclic(X15,X2)
        | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X15,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f366,axiom,
    ! [X2,X15] :
      ( ~ c_Wellfounded_Oacyclic(X15,X2)
      | c_Relation_Oantisym(c_Transitive__Closure_Ortrancl(X15,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).

fof(f1068,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f283,f1066]) ).

fof(f1066,plain,
    ( spl0_57
  <=> ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f283,axiom,
    ! [X2,X1] : c_Lattices_Olower__semilattice__class_Oinf(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

fof(f1064,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f282,f1062]) ).

fof(f282,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Olower__semilattice(X2)
      | c_Lattices_Olower__semilattice__class_Oinf(X4,X4,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1060,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f259,f1058]) ).

fof(f1058,plain,
    ( spl0_55
  <=> ! [X2,X1,X4] : hBOOL(c_in(X4,c_Set_Oinsert(X4,X1,X2),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f259,axiom,
    ! [X2,X1,X4] : hBOOL(c_in(X4,c_Set_Oinsert(X4,X1,X2),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

fof(f1056,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f198,f1054]) ).

fof(f1054,plain,
    ( spl0_54
  <=> ! [X2,X1,X15] :
        ( ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2)
        | c_Relation_Ototal__on(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f198,axiom,
    ! [X2,X1,X15] :
      ( ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2)
      | c_Relation_Ototal__on(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).

fof(f1051,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f187,f1049]) ).

fof(f187,axiom,
    ! [X2] : c_Wellfounded_Owf(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).

fof(f1046,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f140,f1044]) ).

fof(f1044,plain,
    ( spl0_52
  <=> ! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f140,axiom,
    ! [X2] : c_Relation_Oantisym(c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_bool)),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).

fof(f1042,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f45,f1040]) ).

fof(f1040,plain,
    ( spl0_51
  <=> ! [X7,X14,X2,X26] : hAPP(c_COMBK(X14,X2,X7),X26) = X14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f45,axiom,
    ! [X2,X26,X7,X14] : hAPP(c_COMBK(X14,X2,X7),X26) = X14,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1038,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f37,f1036]) ).

fof(f37,axiom,
    ! [X2,X4] :
      ( ~ class_Lattices_Oupper__semilattice(X2)
      | c_Lattices_Oupper__semilattice__class_Osup(X4,X4,X2) = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1034,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f36,f1032]) ).

fof(f1032,plain,
    ( spl0_49
  <=> ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f36,axiom,
    ! [X2,X1] : c_Lattices_Oupper__semilattice__class_Osup(X1,X1,tc_fun(X2,tc_bool)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

fof(f1029,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f697,f1027]) ).

fof(f1027,plain,
    ( spl0_48
  <=> ! [X38,X2,X39] :
        ( X38 = X39
        | ~ c_fequal(X38,X39,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f697,axiom,
    ! [X2,X38,X39] :
      ( X38 = X39
      | ~ c_fequal(X38,X39,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1025,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f545,f1023]) ).

fof(f1023,plain,
    ( spl0_47
  <=> ! [X2,X1,X15] :
        ( c_Relation_Osym(X15,X2)
        | ~ c_Equiv__Relations_Oequiv(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f545,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Osym(X15,X2)
      | ~ c_Equiv__Relations_Oequiv(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).

fof(f1021,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f544,f1019]) ).

fof(f1019,plain,
    ( spl0_46
  <=> ! [X2,X15] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X15,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f544,axiom,
    ! [X2,X15] : c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X15,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).

fof(f1017,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f539,f1015]) ).

fof(f1015,plain,
    ( spl0_45
  <=> ! [X4,X2] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f539,axiom,
    ! [X2,X4] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

fof(f1013,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f380,f1011]) ).

fof(f1011,plain,
    ( spl0_44
  <=> ! [X2,X1,X15] :
        ( c_Relation_Otrans(X15,X2)
        | ~ c_Equiv__Relations_Oequiv(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f380,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Otrans(X15,X2)
      | ~ c_Equiv__Relations_Oequiv(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).

fof(f1009,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f330,f1007]) ).

fof(f1007,plain,
    ( spl0_43
  <=> ! [X2,X1,X15] :
        ( c_Relation_Oirrefl(X15,X2)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f330,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Oirrefl(X15,X2)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).

fof(f1005,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f274,f1003]) ).

fof(f1003,plain,
    ( spl0_42
  <=> ! [X2,X1,X15] :
        ( c_Relation_Otrans(X15,X2)
        | ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f274,axiom,
    ! [X2,X1,X15] :
      ( c_Relation_Otrans(X15,X2)
      | ~ c_Order__Relation_Ostrict__linear__order__on(X1,X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).

fof(f1001,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f171,f999]) ).

fof(f999,plain,
    ( spl0_41
  <=> ! [X4,X2,X1] : hBOOL(hAPP(c_Set_Oinsert(X4,X1,X2),X4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f171,axiom,
    ! [X2,X1,X4] : hBOOL(hAPP(c_Set_Oinsert(X4,X1,X2),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

fof(f997,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f5,f995]) ).

fof(f995,plain,
    ( spl0_40
  <=> ! [X2,X4] :
        ( ~ class_Orderings_Obot(X2)
        | c_lessequals(c_Orderings_Obot__class_Obot(X2),X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f5,axiom,
    ! [X2,X4] :
      ( ~ class_Orderings_Obot(X2)
      | c_lessequals(c_Orderings_Obot__class_Obot(X2),X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

fof(f993,plain,
    ( spl0_37
    | ~ spl0_39
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f755,f825,f990,f981]) ).

fof(f755,plain,
    ( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(duplicate_literal_removal,[],[f671]) ).

fof(f671,axiom,
    ( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_xa,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_13) ).

fof(f988,plain,
    ( spl0_37
    | ~ spl0_38
    | ~ spl0_1 ),
    inference(avatar_split_clause,[],[f752,f825,f985,f981]) ).

fof(f752,plain,
    ( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(duplicate_literal_removal,[],[f673]) ).

fof(f673,axiom,
    ( ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | ~ hBOOL(c_in(c_Pair(v_x,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_15) ).

fof(f979,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f685,f977]) ).

fof(f977,plain,
    ( spl0_36
  <=> ! [X64,X65] :
        ( ~ class_HOL_Oord(X65)
        | class_HOL_Oord(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f685,axiom,
    ! [X65,X64] :
      ( ~ class_HOL_Oord(X65)
      | class_HOL_Oord(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

fof(f975,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f684,f973]) ).

fof(f973,plain,
    ( spl0_35
  <=> ! [X64,X65] :
        ( ~ class_HOL_Ominus(X65)
        | class_HOL_Ominus(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f684,axiom,
    ! [X65,X64] :
      ( ~ class_HOL_Ominus(X65)
      | class_HOL_Ominus(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).

fof(f971,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f683,f969]) ).

fof(f969,plain,
    ( spl0_34
  <=> ! [X64,X65] :
        ( ~ class_Orderings_Obot(X65)
        | class_Orderings_Obot(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f683,axiom,
    ! [X65,X64] :
      ( ~ class_Orderings_Obot(X65)
      | class_Orderings_Obot(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

fof(f967,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f682,f965]) ).

fof(f965,plain,
    ( spl0_33
  <=> ! [X64,X65] :
        ( ~ class_Orderings_Oorder(X65)
        | class_Orderings_Oorder(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f682,axiom,
    ! [X65,X64] :
      ( ~ class_Orderings_Oorder(X65)
      | class_Orderings_Oorder(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

fof(f963,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f681,f961]) ).

fof(f961,plain,
    ( spl0_32
  <=> ! [X64,X65] :
        ( ~ class_Lattices_Olattice(X65)
        | class_Lattices_Olattice(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f681,axiom,
    ! [X65,X64] :
      ( ~ class_Lattices_Olattice(X65)
      | class_Lattices_Olattice(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f959,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f680,f957]) ).

fof(f957,plain,
    ( spl0_31
  <=> ! [X64,X65] :
        ( ~ class_Orderings_Opreorder(X65)
        | class_Orderings_Opreorder(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f680,axiom,
    ! [X65,X64] :
      ( ~ class_Orderings_Opreorder(X65)
      | class_Orderings_Opreorder(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

fof(f955,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f679,f953]) ).

fof(f953,plain,
    ( spl0_30
  <=> ! [X64,X65] :
        ( ~ class_Lattices_Obounded__lattice(X65)
        | class_Lattices_Obounded__lattice(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f679,axiom,
    ! [X65,X64] :
      ( ~ class_Lattices_Obounded__lattice(X65)
      | class_Lattices_Obounded__lattice(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

fof(f951,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f678,f949]) ).

fof(f949,plain,
    ( spl0_29
  <=> ! [X64,X65] :
        ( ~ class_Lattices_Odistrib__lattice(X65)
        | class_Lattices_Odistrib__lattice(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f678,axiom,
    ! [X65,X64] :
      ( ~ class_Lattices_Odistrib__lattice(X65)
      | class_Lattices_Odistrib__lattice(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f947,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f677,f945]) ).

fof(f945,plain,
    ( spl0_28
  <=> ! [X64,X65] :
        ( ~ class_Lattices_Olattice(X65)
        | class_Lattices_Olower__semilattice(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f677,axiom,
    ! [X65,X64] :
      ( ~ class_Lattices_Olattice(X65)
      | class_Lattices_Olower__semilattice(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f943,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f676,f941]) ).

fof(f941,plain,
    ( spl0_27
  <=> ! [X64,X65] :
        ( ~ class_Lattices_Olattice(X65)
        | class_Lattices_Oupper__semilattice(tc_fun(X64,X65)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f676,axiom,
    ! [X65,X64] :
      ( ~ class_Lattices_Olattice(X65)
      | class_Lattices_Oupper__semilattice(tc_fun(X64,X65)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f939,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f514,f937]) ).

fof(f937,plain,
    ( spl0_26
  <=> ! [X2,X1] : c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f514,axiom,
    ! [X2,X1] : c_Relation_Orefl__on(X1,c_Relation_OId__on(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).

fof(f935,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f482,f933]) ).

fof(f933,plain,
    ( spl0_25
  <=> ! [X2,X1] : c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f482,axiom,
    ! [X2,X1] : c_Relation_Osingle__valued(c_Relation_OId__on(X1,X2),X2,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).

fof(f931,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f301,f929]) ).

fof(f929,plain,
    ( spl0_24
  <=> ! [X2,X4] :
        ( ~ class_Orderings_Opreorder(X2)
        | c_lessequals(X4,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f301,axiom,
    ! [X2,X4] :
      ( ~ class_Orderings_Opreorder(X2)
      | c_lessequals(X4,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

fof(f927,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f300,f925]) ).

fof(f925,plain,
    ( spl0_23
  <=> ! [X2,X4] :
        ( ~ class_Orderings_Oorder(X2)
        | c_lessequals(X4,X4,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f300,axiom,
    ! [X2,X4] :
      ( ~ class_Orderings_Oorder(X2)
      | c_lessequals(X4,X4,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

fof(f923,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f296,f921]) ).

fof(f921,plain,
    ( spl0_22
  <=> ! [X2,X1] : c_lessequals(X1,X1,tc_fun(X2,tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f296,axiom,
    ! [X2,X1] : c_lessequals(X1,X1,tc_fun(X2,tc_bool)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

fof(f919,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f177,f917]) ).

fof(f917,plain,
    ( spl0_21
  <=> ! [X2,X15] :
        ( ~ c_Wellfounded_Owf(X15,X2)
        | c_Wellfounded_Oacyclic(X15,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f177,axiom,
    ! [X2,X15] :
      ( ~ c_Wellfounded_Owf(X15,X2)
      | c_Wellfounded_Oacyclic(X15,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).

fof(f915,plain,
    ( spl0_20
    | spl0_20 ),
    inference(avatar_split_clause,[],[f661,f913,f913]) ).

fof(f661,axiom,
    ! [X56,X57] :
      ( ~ hBOOL(c_in(c_Pair(X56,X56,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
      | ~ hBOOL(c_in(c_Pair(X57,X57,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f911,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f562,f909]) ).

fof(f909,plain,
    ( spl0_19
  <=> ! [X2,X1] : c_Relation_Otrans(c_Relation_OId__on(X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f562,axiom,
    ! [X2,X1] : c_Relation_Otrans(c_Relation_OId__on(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).

fof(f907,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f561,f905]) ).

fof(f905,plain,
    ( spl0_18
  <=> ! [X2,X15] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X15,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f561,axiom,
    ! [X2,X15] : c_Relation_Otrans(c_Transitive__Closure_Otrancl(X15,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).

fof(f903,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f560,f901]) ).

fof(f901,plain,
    ( spl0_17
  <=> ! [X2,X15] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X15,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f560,axiom,
    ! [X2,X15] : c_Relation_Otrans(c_Transitive__Closure_Ortrancl(X15,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).

fof(f899,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f513,f897]) ).

fof(f897,plain,
    ( spl0_16
  <=> ! [X2,X1] : c_Relation_Osym(c_Relation_OId__on(X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f513,axiom,
    ! [X2,X1] : c_Relation_Osym(c_Relation_OId__on(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).

fof(f895,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f497,f893]) ).

fof(f893,plain,
    ( spl0_15
  <=> ! [X2,X1] : c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f497,axiom,
    ! [X2,X1] : c_Relation_Oantisym(c_Relation_OId__on(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).

fof(f891,plain,
    ( spl0_13
    | ~ spl0_1
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f762,f888,f825,f884]) ).

fof(f762,plain,
    ( v_x != v_xa
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_xa,v_xa,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(inner_rewriting,[],[f760]) ).

fof(f760,plain,
    ( v_x != v_xa
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    inference(duplicate_literal_removal,[],[f666]) ).

fof(f666,axiom,
    ( v_x != v_xa
    | v_x != v_xa
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | ~ c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)))
    | hBOOL(c_in(c_Pair(v_x,v_x,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_L,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).

fof(f882,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f696,f880]) ).

fof(f880,plain,
    ( spl0_12
  <=> ! [X2,X4] : c_fequal(X4,X4,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f696,axiom,
    ! [X2,X4] : c_fequal(X4,X4,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f878,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f695,f875]) ).

fof(f875,plain,
    ( spl0_11
  <=> class_HOL_Oord(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f695,axiom,
    class_HOL_Oord(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

fof(f873,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f694,f870]) ).

fof(f870,plain,
    ( spl0_10
  <=> class_HOL_Ominus(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f694,axiom,
    class_HOL_Ominus(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).

fof(f868,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f693,f865]) ).

fof(f865,plain,
    ( spl0_9
  <=> class_Orderings_Obot(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f693,axiom,
    class_Orderings_Obot(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

fof(f863,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f692,f860]) ).

fof(f860,plain,
    ( spl0_8
  <=> class_Orderings_Oorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f692,axiom,
    class_Orderings_Oorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

fof(f858,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f691,f855]) ).

fof(f691,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f853,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f690,f850]) ).

fof(f850,plain,
    ( spl0_6
  <=> class_Orderings_Opreorder(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f690,axiom,
    class_Orderings_Opreorder(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

fof(f848,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f689,f845]) ).

fof(f689,axiom,
    class_Lattices_Obounded__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

fof(f843,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f688,f840]) ).

fof(f840,plain,
    ( spl0_4
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f688,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f838,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f687,f835]) ).

fof(f687,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f833,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f686,f830]) ).

fof(f686,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f828,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f761,f825]) ).

fof(f761,plain,
    c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt),
    inference(duplicate_literal_removal,[],[f658]) ).

fof(f658,axiom,
    ( c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt)
    | c_Relation_Otrans(v_L,tc_Arrow__Order__Mirabelle_Oalt) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SCT004-1 : TPTP v8.1.2. Released v4.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36  % Computer : n004.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Fri May  3 12:56:48 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.13/0.36  % (15336)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.42  % (15339)WARNING: value z3 for option sas not known
% 0.19/0.42  % (15338)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.42  % (15340)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.42  % (15339)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)
% 0.19/0.42  % (15341)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)
% 0.19/0.42  % (15343)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)
% 0.19/0.42  % (15342)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)
% 0.19/0.42  % (15337)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.47  % (15341)First to succeed.
% 0.19/0.48  % (15341)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15336"
% 0.19/0.48  % (15341)Refutation found. Thanks to Tanya!
% 0.19/0.48  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (15341)------------------------------
% 0.19/0.48  % (15341)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.48  % (15341)Termination reason: Refutation
% 0.19/0.48  
% 0.19/0.48  % (15341)Memory used [KB]: 1978
% 0.19/0.48  % (15341)Time elapsed: 0.059 s
% 0.19/0.48  % (15341)Instructions burned: 109 (million)
% 0.19/0.48  % (15336)Success in time 0.115 s
%------------------------------------------------------------------------------