TSTP Solution File: NUM410+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n016.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 : Tue Apr 30 14:21:59 EDT 2024

% Result   : Theorem 0.12s 0.31s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  184
% Syntax   : Number of formulae    :  538 ( 139 unt;   0 def)
%            Number of atoms       : 1389 (  42 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 1413 ( 562   ~; 523   |; 158   &)
%                                         ( 132 <=>;  38  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :  141 ( 139 usr; 126 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  16 con; 0-1 aty)
%            Number of variables   :  343 ( 303   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f984,plain,
    $false,
    inference(avatar_sat_refutation,[],[f215,f220,f225,f230,f235,f240,f245,f250,f255,f260,f265,f270,f275,f280,f285,f290,f295,f300,f305,f310,f315,f320,f325,f330,f335,f340,f345,f350,f355,f360,f365,f370,f375,f380,f385,f390,f395,f400,f405,f410,f415,f420,f425,f430,f434,f438,f442,f446,f450,f454,f458,f462,f466,f470,f480,f514,f518,f522,f526,f530,f534,f538,f542,f546,f566,f580,f584,f588,f597,f601,f605,f609,f613,f621,f636,f642,f646,f650,f662,f666,f672,f676,f684,f690,f695,f700,f706,f712,f717,f723,f729,f734,f740,f749,f754,f759,f764,f768,f772,f776,f797,f801,f805,f809,f813,f817,f821,f825,f829,f833,f851,f855,f859,f888,f894,f898,f902,f906,f910,f950,f954,f959,f963,f971,f975,f983]) ).

fof(f983,plain,
    ( ~ spl17_1
    | ~ spl17_2
    | ~ spl17_79
    | spl17_4
    | ~ spl17_125 ),
    inference(avatar_split_clause,[],[f979,f973,f227,f659,f217,f212]) ).

fof(f212,plain,
    ( spl17_1
  <=> relation(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).

fof(f217,plain,
    ( spl17_2
  <=> function(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).

fof(f659,plain,
    ( spl17_79
  <=> transfinite_sequence(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).

fof(f227,plain,
    ( spl17_4
  <=> transfinite_sequence_of(sK0,relation_rng(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f973,plain,
    ( spl17_125
  <=> ! [X0] :
        ( transfinite_sequence_of(X0,relation_rng(X0))
        | ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_125])]) ).

fof(f979,plain,
    ( ~ transfinite_sequence(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | spl17_4
    | ~ spl17_125 ),
    inference(resolution,[],[f974,f229]) ).

fof(f229,plain,
    ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
    | spl17_4 ),
    inference(avatar_component_clause,[],[f227]) ).

fof(f974,plain,
    ( ! [X0] :
        ( transfinite_sequence_of(X0,relation_rng(X0))
        | ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl17_125 ),
    inference(avatar_component_clause,[],[f973]) ).

fof(f975,plain,
    ( spl17_125
    | ~ spl17_45
    | ~ spl17_82 ),
    inference(avatar_split_clause,[],[f678,f674,f432,f973]) ).

fof(f432,plain,
    ( spl17_45
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).

fof(f674,plain,
    ( spl17_82
  <=> ! [X0,X1] :
        ( transfinite_sequence_of(X1,X0)
        | ~ subset(relation_rng(X1),X0)
        | ~ transfinite_sequence(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).

fof(f678,plain,
    ( ! [X0] :
        ( transfinite_sequence_of(X0,relation_rng(X0))
        | ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl17_45
    | ~ spl17_82 ),
    inference(resolution,[],[f675,f433]) ).

fof(f433,plain,
    ( ! [X0] : subset(X0,X0)
    | ~ spl17_45 ),
    inference(avatar_component_clause,[],[f432]) ).

fof(f675,plain,
    ( ! [X0,X1] :
        ( ~ subset(relation_rng(X1),X0)
        | transfinite_sequence_of(X1,X0)
        | ~ transfinite_sequence(X1)
        | ~ function(X1)
        | ~ relation(X1) )
    | ~ spl17_82 ),
    inference(avatar_component_clause,[],[f674]) ).

fof(f971,plain,
    ( spl17_124
    | ~ spl17_72
    | ~ spl17_75 ),
    inference(avatar_split_clause,[],[f638,f634,f607,f969]) ).

fof(f969,plain,
    ( spl17_124
  <=> ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).

fof(f607,plain,
    ( spl17_72
  <=> ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).

fof(f634,plain,
    ( spl17_75
  <=> ! [X0,X1] :
        ( in(X0,X1)
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).

fof(f638,plain,
    ( ! [X0,X1] :
        ( empty(powerset(X0))
        | in(X1,powerset(X0))
        | ~ subset(X1,X0) )
    | ~ spl17_72
    | ~ spl17_75 ),
    inference(resolution,[],[f635,f608]) ).

fof(f608,plain,
    ( ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
    | ~ spl17_72 ),
    inference(avatar_component_clause,[],[f607]) ).

fof(f635,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,X1)
        | empty(X1)
        | in(X0,X1) )
    | ~ spl17_75 ),
    inference(avatar_component_clause,[],[f634]) ).

fof(f963,plain,
    ( spl17_123
    | ~ spl17_72
    | ~ spl17_80 ),
    inference(avatar_split_clause,[],[f668,f664,f607,f961]) ).

fof(f961,plain,
    ( spl17_123
  <=> ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).

fof(f664,plain,
    ( spl17_80
  <=> ! [X2,X0,X1] :
        ( element(X0,X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).

fof(f668,plain,
    ( ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) )
    | ~ spl17_72
    | ~ spl17_80 ),
    inference(resolution,[],[f665,f608]) ).

fof(f665,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | element(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl17_80 ),
    inference(avatar_component_clause,[],[f664]) ).

fof(f959,plain,
    ( spl17_122
    | ~ spl17_5
    | ~ spl17_94
    | ~ spl17_112 ),
    inference(avatar_split_clause,[],[f878,f853,f746,f232,f956]) ).

fof(f956,plain,
    ( spl17_122
  <=> sK4 = relation_rng(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).

fof(f232,plain,
    ( spl17_5
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).

fof(f746,plain,
    ( spl17_94
  <=> empty_set = sK4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).

fof(f853,plain,
    ( spl17_112
  <=> ! [X0] :
        ( relation_rng(X0) = sK4
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).

fof(f878,plain,
    ( sK4 = relation_rng(sK4)
    | ~ spl17_5
    | ~ spl17_94
    | ~ spl17_112 ),
    inference(forward_demodulation,[],[f873,f748]) ).

fof(f748,plain,
    ( empty_set = sK4
    | ~ spl17_94 ),
    inference(avatar_component_clause,[],[f746]) ).

fof(f873,plain,
    ( sK4 = relation_rng(empty_set)
    | ~ spl17_5
    | ~ spl17_112 ),
    inference(resolution,[],[f854,f234]) ).

fof(f234,plain,
    ( empty(empty_set)
    | ~ spl17_5 ),
    inference(avatar_component_clause,[],[f232]) ).

fof(f854,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_rng(X0) = sK4 )
    | ~ spl17_112 ),
    inference(avatar_component_clause,[],[f853]) ).

fof(f954,plain,
    ( spl17_121
    | ~ spl17_46
    | ~ spl17_76 ),
    inference(avatar_split_clause,[],[f652,f640,f436,f952]) ).

fof(f952,plain,
    ( spl17_121
  <=> ! [X0] :
        ( ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | epsilon_transitive(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).

fof(f436,plain,
    ( spl17_46
  <=> ! [X0] :
        ( epsilon_transitive(X0)
        | ~ ordinal(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).

fof(f640,plain,
    ( spl17_76
  <=> ! [X0] :
        ( ordinal(relation_dom(X0))
        | ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).

fof(f652,plain,
    ( ! [X0] :
        ( ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | epsilon_transitive(relation_dom(X0)) )
    | ~ spl17_46
    | ~ spl17_76 ),
    inference(resolution,[],[f641,f437]) ).

fof(f437,plain,
    ( ! [X0] :
        ( ~ ordinal(X0)
        | epsilon_transitive(X0) )
    | ~ spl17_46 ),
    inference(avatar_component_clause,[],[f436]) ).

fof(f641,plain,
    ( ! [X0] :
        ( ordinal(relation_dom(X0))
        | ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl17_76 ),
    inference(avatar_component_clause,[],[f640]) ).

fof(f950,plain,
    ( spl17_120
    | ~ spl17_47
    | ~ spl17_76 ),
    inference(avatar_split_clause,[],[f651,f640,f440,f948]) ).

fof(f948,plain,
    ( spl17_120
  <=> ! [X0] :
        ( ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | epsilon_connected(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).

fof(f440,plain,
    ( spl17_47
  <=> ! [X0] :
        ( epsilon_connected(X0)
        | ~ ordinal(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).

fof(f651,plain,
    ( ! [X0] :
        ( ~ transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0)
        | epsilon_connected(relation_dom(X0)) )
    | ~ spl17_47
    | ~ spl17_76 ),
    inference(resolution,[],[f641,f441]) ).

fof(f441,plain,
    ( ! [X0] :
        ( ~ ordinal(X0)
        | epsilon_connected(X0) )
    | ~ spl17_47 ),
    inference(avatar_component_clause,[],[f440]) ).

fof(f910,plain,
    ( spl17_119
    | ~ spl17_54
    | ~ spl17_80 ),
    inference(avatar_split_clause,[],[f667,f664,f468,f908]) ).

fof(f908,plain,
    ( spl17_119
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK2(powerset(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).

fof(f468,plain,
    ( spl17_54
  <=> ! [X0] : element(sK2(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).

fof(f667,plain,
    ( ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK2(powerset(X1))) )
    | ~ spl17_54
    | ~ spl17_80 ),
    inference(resolution,[],[f665,f469]) ).

fof(f469,plain,
    ( ! [X0] : element(sK2(X0),X0)
    | ~ spl17_54 ),
    inference(avatar_component_clause,[],[f468]) ).

fof(f906,plain,
    ( spl17_118
    | ~ spl17_72
    | ~ spl17_78 ),
    inference(avatar_split_clause,[],[f657,f648,f607,f904]) ).

fof(f904,plain,
    ( spl17_118
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).

fof(f648,plain,
    ( spl17_78
  <=> ! [X2,X0,X1] :
        ( ~ empty(X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).

fof(f657,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) )
    | ~ spl17_72
    | ~ spl17_78 ),
    inference(resolution,[],[f649,f608]) ).

fof(f649,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | ~ empty(X2)
        | ~ in(X0,X1) )
    | ~ spl17_78 ),
    inference(avatar_component_clause,[],[f648]) ).

fof(f902,plain,
    ( spl17_117
    | ~ spl17_59
    | ~ spl17_73 ),
    inference(avatar_split_clause,[],[f624,f611,f524,f900]) ).

fof(f900,plain,
    ( spl17_117
  <=> ! [X0,X1] :
        ( relation_rng(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).

fof(f524,plain,
    ( spl17_59
  <=> ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).

fof(f611,plain,
    ( spl17_73
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).

fof(f624,plain,
    ( ! [X0,X1] :
        ( relation_rng(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl17_59
    | ~ spl17_73 ),
    inference(resolution,[],[f612,f525]) ).

fof(f525,plain,
    ( ! [X0] :
        ( empty(relation_rng(X0))
        | ~ empty(X0) )
    | ~ spl17_59 ),
    inference(avatar_component_clause,[],[f524]) ).

fof(f612,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl17_73 ),
    inference(avatar_component_clause,[],[f611]) ).

fof(f898,plain,
    ( spl17_116
    | ~ spl17_57
    | ~ spl17_73 ),
    inference(avatar_split_clause,[],[f623,f611,f516,f896]) ).

fof(f896,plain,
    ( spl17_116
  <=> ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).

fof(f516,plain,
    ( spl17_57
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).

fof(f623,plain,
    ( ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl17_57
    | ~ spl17_73 ),
    inference(resolution,[],[f612,f517]) ).

fof(f517,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl17_57 ),
    inference(avatar_component_clause,[],[f516]) ).

fof(f894,plain,
    ( spl17_115
    | ~ spl17_5
    | ~ spl17_94
    | ~ spl17_111 ),
    inference(avatar_split_clause,[],[f867,f849,f746,f232,f891]) ).

fof(f891,plain,
    ( spl17_115
  <=> sK4 = relation_dom(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).

fof(f849,plain,
    ( spl17_111
  <=> ! [X0] :
        ( relation_dom(X0) = sK4
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).

fof(f867,plain,
    ( sK4 = relation_dom(sK4)
    | ~ spl17_5
    | ~ spl17_94
    | ~ spl17_111 ),
    inference(forward_demodulation,[],[f862,f748]) ).

fof(f862,plain,
    ( sK4 = relation_dom(empty_set)
    | ~ spl17_5
    | ~ spl17_111 ),
    inference(resolution,[],[f850,f234]) ).

fof(f850,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_dom(X0) = sK4 )
    | ~ spl17_111 ),
    inference(avatar_component_clause,[],[f849]) ).

fof(f888,plain,
    ( spl17_114
    | ~ spl17_54
    | ~ spl17_78 ),
    inference(avatar_split_clause,[],[f656,f648,f468,f886]) ).

fof(f886,plain,
    ( spl17_114
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK2(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).

fof(f656,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK2(powerset(X0))) )
    | ~ spl17_54
    | ~ spl17_78 ),
    inference(resolution,[],[f649,f469]) ).

fof(f859,plain,
    ( spl17_113
    | ~ spl17_54
    | ~ spl17_75 ),
    inference(avatar_split_clause,[],[f637,f634,f468,f857]) ).

fof(f857,plain,
    ( spl17_113
  <=> ! [X0] :
        ( empty(X0)
        | in(sK2(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).

fof(f637,plain,
    ( ! [X0] :
        ( empty(X0)
        | in(sK2(X0),X0) )
    | ~ spl17_54
    | ~ spl17_75 ),
    inference(resolution,[],[f635,f469]) ).

fof(f855,plain,
    ( spl17_112
    | ~ spl17_12
    | ~ spl17_56
    | ~ spl17_59 ),
    inference(avatar_split_clause,[],[f573,f524,f512,f267,f853]) ).

fof(f267,plain,
    ( spl17_12
  <=> empty(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).

fof(f512,plain,
    ( spl17_56
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).

fof(f573,plain,
    ( ! [X0] :
        ( relation_rng(X0) = sK4
        | ~ empty(X0) )
    | ~ spl17_12
    | ~ spl17_56
    | ~ spl17_59 ),
    inference(forward_demodulation,[],[f567,f548]) ).

fof(f548,plain,
    ( empty_set = sK4
    | ~ spl17_12
    | ~ spl17_56 ),
    inference(resolution,[],[f513,f269]) ).

fof(f269,plain,
    ( empty(sK4)
    | ~ spl17_12 ),
    inference(avatar_component_clause,[],[f267]) ).

fof(f513,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl17_56 ),
    inference(avatar_component_clause,[],[f512]) ).

fof(f567,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_rng(X0) )
    | ~ spl17_56
    | ~ spl17_59 ),
    inference(resolution,[],[f525,f513]) ).

fof(f851,plain,
    ( spl17_111
    | ~ spl17_12
    | ~ spl17_56
    | ~ spl17_57 ),
    inference(avatar_split_clause,[],[f561,f516,f512,f267,f849]) ).

fof(f561,plain,
    ( ! [X0] :
        ( relation_dom(X0) = sK4
        | ~ empty(X0) )
    | ~ spl17_12
    | ~ spl17_56
    | ~ spl17_57 ),
    inference(forward_demodulation,[],[f555,f548]) ).

fof(f555,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation_dom(X0) = empty_set )
    | ~ spl17_56
    | ~ spl17_57 ),
    inference(resolution,[],[f517,f513]) ).

fof(f833,plain,
    ( spl17_110
    | ~ spl17_12
    | ~ spl17_73 ),
    inference(avatar_split_clause,[],[f626,f611,f267,f831]) ).

fof(f831,plain,
    ( spl17_110
  <=> ! [X0] :
        ( sK4 = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).

fof(f626,plain,
    ( ! [X0] :
        ( sK4 = X0
        | ~ empty(X0) )
    | ~ spl17_12
    | ~ spl17_73 ),
    inference(resolution,[],[f612,f269]) ).

fof(f829,plain,
    ( spl17_109
    | ~ spl17_54
    | ~ spl17_71 ),
    inference(avatar_split_clause,[],[f616,f603,f468,f827]) ).

fof(f827,plain,
    ( spl17_109
  <=> ! [X0] : subset(sK2(powerset(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).

fof(f603,plain,
    ( spl17_71
  <=> ! [X0,X1] :
        ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).

fof(f616,plain,
    ( ! [X0] : subset(sK2(powerset(X0)),X0)
    | ~ spl17_54
    | ~ spl17_71 ),
    inference(resolution,[],[f604,f469]) ).

fof(f604,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,powerset(X1))
        | subset(X0,X1) )
    | ~ spl17_71 ),
    inference(avatar_component_clause,[],[f603]) ).

fof(f825,plain,
    ( spl17_108
    | ~ spl17_48
    | ~ spl17_59 ),
    inference(avatar_split_clause,[],[f572,f524,f444,f823]) ).

fof(f823,plain,
    ( spl17_108
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).

fof(f444,plain,
    ( spl17_48
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).

fof(f572,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(relation_rng(X0)) )
    | ~ spl17_48
    | ~ spl17_59 ),
    inference(resolution,[],[f525,f445]) ).

fof(f445,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(X0) )
    | ~ spl17_48 ),
    inference(avatar_component_clause,[],[f444]) ).

fof(f821,plain,
    ( spl17_107
    | ~ spl17_50
    | ~ spl17_59 ),
    inference(avatar_split_clause,[],[f570,f524,f452,f819]) ).

fof(f819,plain,
    ( spl17_107
  <=> ! [X0] :
        ( ~ empty(X0)
        | epsilon_transitive(relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).

fof(f452,plain,
    ( spl17_50
  <=> ! [X0] :
        ( epsilon_transitive(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).

fof(f570,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_transitive(relation_rng(X0)) )
    | ~ spl17_50
    | ~ spl17_59 ),
    inference(resolution,[],[f525,f453]) ).

fof(f453,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_transitive(X0) )
    | ~ spl17_50 ),
    inference(avatar_component_clause,[],[f452]) ).

fof(f817,plain,
    ( spl17_106
    | ~ spl17_51
    | ~ spl17_59 ),
    inference(avatar_split_clause,[],[f569,f524,f456,f815]) ).

fof(f815,plain,
    ( spl17_106
  <=> ! [X0] :
        ( ~ empty(X0)
        | epsilon_connected(relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).

fof(f456,plain,
    ( spl17_51
  <=> ! [X0] :
        ( epsilon_connected(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).

fof(f569,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_connected(relation_rng(X0)) )
    | ~ spl17_51
    | ~ spl17_59 ),
    inference(resolution,[],[f525,f457]) ).

fof(f457,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_connected(X0) )
    | ~ spl17_51 ),
    inference(avatar_component_clause,[],[f456]) ).

fof(f813,plain,
    ( spl17_105
    | ~ spl17_52
    | ~ spl17_59 ),
    inference(avatar_split_clause,[],[f568,f524,f460,f811]) ).

fof(f811,plain,
    ( spl17_105
  <=> ! [X0] :
        ( ~ empty(X0)
        | ordinal(relation_rng(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).

fof(f460,plain,
    ( spl17_52
  <=> ! [X0] :
        ( ordinal(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).

fof(f568,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ordinal(relation_rng(X0)) )
    | ~ spl17_52
    | ~ spl17_59 ),
    inference(resolution,[],[f525,f461]) ).

fof(f461,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ordinal(X0) )
    | ~ spl17_52 ),
    inference(avatar_component_clause,[],[f460]) ).

fof(f809,plain,
    ( spl17_104
    | ~ spl17_48
    | ~ spl17_57 ),
    inference(avatar_split_clause,[],[f560,f516,f444,f807]) ).

fof(f807,plain,
    ( spl17_104
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).

fof(f560,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) )
    | ~ spl17_48
    | ~ spl17_57 ),
    inference(resolution,[],[f517,f445]) ).

fof(f805,plain,
    ( spl17_103
    | ~ spl17_50
    | ~ spl17_57 ),
    inference(avatar_split_clause,[],[f558,f516,f452,f803]) ).

fof(f803,plain,
    ( spl17_103
  <=> ! [X0] :
        ( ~ empty(X0)
        | epsilon_transitive(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).

fof(f558,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_transitive(relation_dom(X0)) )
    | ~ spl17_50
    | ~ spl17_57 ),
    inference(resolution,[],[f517,f453]) ).

fof(f801,plain,
    ( spl17_102
    | ~ spl17_51
    | ~ spl17_57 ),
    inference(avatar_split_clause,[],[f557,f516,f456,f799]) ).

fof(f799,plain,
    ( spl17_102
  <=> ! [X0] :
        ( ~ empty(X0)
        | epsilon_connected(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).

fof(f557,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | epsilon_connected(relation_dom(X0)) )
    | ~ spl17_51
    | ~ spl17_57 ),
    inference(resolution,[],[f517,f457]) ).

fof(f797,plain,
    ( spl17_101
    | ~ spl17_52
    | ~ spl17_57 ),
    inference(avatar_split_clause,[],[f556,f516,f460,f795]) ).

fof(f795,plain,
    ( spl17_101
  <=> ! [X0] :
        ( ~ empty(X0)
        | ordinal(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).

fof(f556,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | ordinal(relation_dom(X0)) )
    | ~ spl17_52
    | ~ spl17_57 ),
    inference(resolution,[],[f517,f461]) ).

fof(f776,plain,
    ( spl17_100
    | ~ spl17_53
    | ~ spl17_63 ),
    inference(avatar_split_clause,[],[f576,f540,f464,f774]) ).

fof(f774,plain,
    ( spl17_100
  <=> ! [X0] : transfinite_sequence(sK1(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).

fof(f464,plain,
    ( spl17_53
  <=> ! [X0] : transfinite_sequence_of(sK1(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).

fof(f540,plain,
    ( spl17_63
  <=> ! [X0,X1] :
        ( transfinite_sequence(X1)
        | ~ transfinite_sequence_of(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).

fof(f576,plain,
    ( ! [X0] : transfinite_sequence(sK1(X0))
    | ~ spl17_53
    | ~ spl17_63 ),
    inference(resolution,[],[f541,f465]) ).

fof(f465,plain,
    ( ! [X0] : transfinite_sequence_of(sK1(X0),X0)
    | ~ spl17_53 ),
    inference(avatar_component_clause,[],[f464]) ).

fof(f541,plain,
    ( ! [X0,X1] :
        ( ~ transfinite_sequence_of(X1,X0)
        | transfinite_sequence(X1) )
    | ~ spl17_63 ),
    inference(avatar_component_clause,[],[f540]) ).

fof(f772,plain,
    ( spl17_99
    | ~ spl17_53
    | ~ spl17_62 ),
    inference(avatar_split_clause,[],[f575,f536,f464,f770]) ).

fof(f770,plain,
    ( spl17_99
  <=> ! [X0] : function(sK1(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).

fof(f536,plain,
    ( spl17_62
  <=> ! [X0,X1] :
        ( function(X1)
        | ~ transfinite_sequence_of(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).

fof(f575,plain,
    ( ! [X0] : function(sK1(X0))
    | ~ spl17_53
    | ~ spl17_62 ),
    inference(resolution,[],[f537,f465]) ).

fof(f537,plain,
    ( ! [X0,X1] :
        ( ~ transfinite_sequence_of(X1,X0)
        | function(X1) )
    | ~ spl17_62 ),
    inference(avatar_component_clause,[],[f536]) ).

fof(f768,plain,
    ( spl17_98
    | ~ spl17_53
    | ~ spl17_61 ),
    inference(avatar_split_clause,[],[f574,f532,f464,f766]) ).

fof(f766,plain,
    ( spl17_98
  <=> ! [X0] : relation(sK1(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).

fof(f532,plain,
    ( spl17_61
  <=> ! [X0,X1] :
        ( relation(X1)
        | ~ transfinite_sequence_of(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).

fof(f574,plain,
    ( ! [X0] : relation(sK1(X0))
    | ~ spl17_53
    | ~ spl17_61 ),
    inference(resolution,[],[f533,f465]) ).

fof(f533,plain,
    ( ! [X0,X1] :
        ( ~ transfinite_sequence_of(X1,X0)
        | relation(X1) )
    | ~ spl17_61 ),
    inference(avatar_component_clause,[],[f532]) ).

fof(f764,plain,
    ( spl17_97
    | ~ spl17_12
    | ~ spl17_43
    | ~ spl17_56 ),
    inference(avatar_split_clause,[],[f554,f512,f422,f267,f761]) ).

fof(f761,plain,
    ( spl17_97
  <=> sK4 = sK16 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).

fof(f422,plain,
    ( spl17_43
  <=> empty(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).

fof(f554,plain,
    ( sK4 = sK16
    | ~ spl17_12
    | ~ spl17_43
    | ~ spl17_56 ),
    inference(forward_demodulation,[],[f551,f548]) ).

fof(f551,plain,
    ( empty_set = sK16
    | ~ spl17_43
    | ~ spl17_56 ),
    inference(resolution,[],[f513,f424]) ).

fof(f424,plain,
    ( empty(sK16)
    | ~ spl17_43 ),
    inference(avatar_component_clause,[],[f422]) ).

fof(f759,plain,
    ( spl17_96
    | ~ spl17_12
    | ~ spl17_38
    | ~ spl17_56 ),
    inference(avatar_split_clause,[],[f553,f512,f397,f267,f756]) ).

fof(f756,plain,
    ( spl17_96
  <=> sK4 = sK15 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).

fof(f397,plain,
    ( spl17_38
  <=> empty(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).

fof(f553,plain,
    ( sK4 = sK15
    | ~ spl17_12
    | ~ spl17_38
    | ~ spl17_56 ),
    inference(forward_demodulation,[],[f550,f548]) ).

fof(f550,plain,
    ( empty_set = sK15
    | ~ spl17_38
    | ~ spl17_56 ),
    inference(resolution,[],[f513,f399]) ).

fof(f399,plain,
    ( empty(sK15)
    | ~ spl17_38 ),
    inference(avatar_component_clause,[],[f397]) ).

fof(f754,plain,
    ( spl17_95
    | ~ spl17_12
    | ~ spl17_22
    | ~ spl17_56 ),
    inference(avatar_split_clause,[],[f552,f512,f317,f267,f751]) ).

fof(f751,plain,
    ( spl17_95
  <=> sK4 = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).

fof(f317,plain,
    ( spl17_22
  <=> empty(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).

fof(f552,plain,
    ( sK4 = sK8
    | ~ spl17_12
    | ~ spl17_22
    | ~ spl17_56 ),
    inference(forward_demodulation,[],[f549,f548]) ).

fof(f549,plain,
    ( empty_set = sK8
    | ~ spl17_22
    | ~ spl17_56 ),
    inference(resolution,[],[f513,f319]) ).

fof(f319,plain,
    ( empty(sK8)
    | ~ spl17_22 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f749,plain,
    ( spl17_94
    | ~ spl17_12
    | ~ spl17_56 ),
    inference(avatar_split_clause,[],[f548,f512,f267,f746]) ).

fof(f740,plain,
    ( spl17_93
    | ~ spl17_43
    | ~ spl17_52 ),
    inference(avatar_split_clause,[],[f510,f460,f422,f737]) ).

fof(f737,plain,
    ( spl17_93
  <=> ordinal(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).

fof(f510,plain,
    ( ordinal(sK16)
    | ~ spl17_43
    | ~ spl17_52 ),
    inference(resolution,[],[f461,f424]) ).

fof(f734,plain,
    ( spl17_92
    | ~ spl17_22
    | ~ spl17_52 ),
    inference(avatar_split_clause,[],[f508,f460,f317,f731]) ).

fof(f731,plain,
    ( spl17_92
  <=> ordinal(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).

fof(f508,plain,
    ( ordinal(sK8)
    | ~ spl17_22
    | ~ spl17_52 ),
    inference(resolution,[],[f461,f319]) ).

fof(f729,plain,
    ( spl17_91
    | ~ spl17_12
    | ~ spl17_52 ),
    inference(avatar_split_clause,[],[f507,f460,f267,f726]) ).

fof(f726,plain,
    ( spl17_91
  <=> ordinal(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).

fof(f507,plain,
    ( ordinal(sK4)
    | ~ spl17_12
    | ~ spl17_52 ),
    inference(resolution,[],[f461,f269]) ).

fof(f723,plain,
    ( spl17_90
    | ~ spl17_43
    | ~ spl17_51 ),
    inference(avatar_split_clause,[],[f505,f456,f422,f720]) ).

fof(f720,plain,
    ( spl17_90
  <=> epsilon_connected(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).

fof(f505,plain,
    ( epsilon_connected(sK16)
    | ~ spl17_43
    | ~ spl17_51 ),
    inference(resolution,[],[f457,f424]) ).

fof(f717,plain,
    ( spl17_89
    | ~ spl17_22
    | ~ spl17_51 ),
    inference(avatar_split_clause,[],[f503,f456,f317,f714]) ).

fof(f714,plain,
    ( spl17_89
  <=> epsilon_connected(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).

fof(f503,plain,
    ( epsilon_connected(sK8)
    | ~ spl17_22
    | ~ spl17_51 ),
    inference(resolution,[],[f457,f319]) ).

fof(f712,plain,
    ( spl17_88
    | ~ spl17_12
    | ~ spl17_51 ),
    inference(avatar_split_clause,[],[f502,f456,f267,f709]) ).

fof(f709,plain,
    ( spl17_88
  <=> epsilon_connected(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).

fof(f502,plain,
    ( epsilon_connected(sK4)
    | ~ spl17_12
    | ~ spl17_51 ),
    inference(resolution,[],[f457,f269]) ).

fof(f706,plain,
    ( spl17_87
    | ~ spl17_43
    | ~ spl17_50 ),
    inference(avatar_split_clause,[],[f500,f452,f422,f703]) ).

fof(f703,plain,
    ( spl17_87
  <=> epsilon_transitive(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).

fof(f500,plain,
    ( epsilon_transitive(sK16)
    | ~ spl17_43
    | ~ spl17_50 ),
    inference(resolution,[],[f453,f424]) ).

fof(f700,plain,
    ( spl17_86
    | ~ spl17_22
    | ~ spl17_50 ),
    inference(avatar_split_clause,[],[f498,f452,f317,f697]) ).

fof(f697,plain,
    ( spl17_86
  <=> epsilon_transitive(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).

fof(f498,plain,
    ( epsilon_transitive(sK8)
    | ~ spl17_22
    | ~ spl17_50 ),
    inference(resolution,[],[f453,f319]) ).

fof(f695,plain,
    ( spl17_85
    | ~ spl17_12
    | ~ spl17_50 ),
    inference(avatar_split_clause,[],[f497,f452,f267,f692]) ).

fof(f692,plain,
    ( spl17_85
  <=> epsilon_transitive(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).

fof(f497,plain,
    ( epsilon_transitive(sK4)
    | ~ spl17_12
    | ~ spl17_50 ),
    inference(resolution,[],[f453,f269]) ).

fof(f690,plain,
    ( spl17_84
    | ~ spl17_12
    | ~ spl17_49 ),
    inference(avatar_split_clause,[],[f492,f448,f267,f687]) ).

fof(f687,plain,
    ( spl17_84
  <=> relation(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).

fof(f448,plain,
    ( spl17_49
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).

fof(f492,plain,
    ( relation(sK4)
    | ~ spl17_12
    | ~ spl17_49 ),
    inference(resolution,[],[f449,f269]) ).

fof(f449,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(X0) )
    | ~ spl17_49 ),
    inference(avatar_component_clause,[],[f448]) ).

fof(f684,plain,
    ( spl17_83
    | ~ spl17_22
    | ~ spl17_48 ),
    inference(avatar_split_clause,[],[f488,f444,f317,f681]) ).

fof(f681,plain,
    ( spl17_83
  <=> function(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).

fof(f488,plain,
    ( function(sK8)
    | ~ spl17_22
    | ~ spl17_48 ),
    inference(resolution,[],[f445,f319]) ).

fof(f676,plain,
    spl17_82,
    inference(avatar_split_clause,[],[f170,f674]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( transfinite_sequence_of(X1,X0)
      | ~ subset(relation_rng(X1),X0)
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( ( transfinite_sequence_of(X1,X0)
          | ~ subset(relation_rng(X1),X0) )
        & ( subset(relation_rng(X1),X0)
          | ~ transfinite_sequence_of(X1,X0) ) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) )
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( transfinite_sequence(X1)
        & function(X1)
        & relation(X1) )
     => ( transfinite_sequence_of(X1,X0)
      <=> subset(relation_rng(X1),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).

fof(f672,plain,
    spl17_81,
    inference(avatar_split_clause,[],[f169,f670]) ).

fof(f670,plain,
    ( spl17_81
  <=> ! [X0,X1] :
        ( subset(relation_rng(X1),X0)
        | ~ transfinite_sequence_of(X1,X0)
        | ~ transfinite_sequence(X1)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( subset(relation_rng(X1),X0)
      | ~ transfinite_sequence_of(X1,X0)
      | ~ transfinite_sequence(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f666,plain,
    spl17_80,
    inference(avatar_split_clause,[],[f175,f664]) ).

fof(f175,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f662,plain,
    ( ~ spl17_1
    | ~ spl17_2
    | spl17_79
    | ~ spl17_3
    | ~ spl17_77 ),
    inference(avatar_split_clause,[],[f653,f644,f222,f659,f217,f212]) ).

fof(f222,plain,
    ( spl17_3
  <=> ordinal(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).

fof(f644,plain,
    ( spl17_77
  <=> ! [X0] :
        ( transfinite_sequence(X0)
        | ~ ordinal(relation_dom(X0))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).

fof(f653,plain,
    ( transfinite_sequence(sK0)
    | ~ function(sK0)
    | ~ relation(sK0)
    | ~ spl17_3
    | ~ spl17_77 ),
    inference(resolution,[],[f645,f224]) ).

fof(f224,plain,
    ( ordinal(relation_dom(sK0))
    | ~ spl17_3 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f645,plain,
    ( ! [X0] :
        ( ~ ordinal(relation_dom(X0))
        | transfinite_sequence(X0)
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl17_77 ),
    inference(avatar_component_clause,[],[f644]) ).

fof(f650,plain,
    spl17_78,
    inference(avatar_split_clause,[],[f176,f648]) ).

fof(f176,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f646,plain,
    spl17_77,
    inference(avatar_split_clause,[],[f157,f644]) ).

fof(f157,plain,
    ! [X0] :
      ( transfinite_sequence(X0)
      | ~ ordinal(relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0] :
      ( ( ( transfinite_sequence(X0)
          | ~ ordinal(relation_dom(X0)) )
        & ( ordinal(relation_dom(X0))
          | ~ transfinite_sequence(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( transfinite_sequence(X0)
      <=> ordinal(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).

fof(f642,plain,
    spl17_76,
    inference(avatar_split_clause,[],[f156,f640]) ).

fof(f156,plain,
    ! [X0] :
      ( ordinal(relation_dom(X0))
      | ~ transfinite_sequence(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f636,plain,
    spl17_75,
    inference(avatar_split_clause,[],[f168,f634]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f621,plain,
    ( spl17_74
    | ~ spl17_12
    | ~ spl17_48 ),
    inference(avatar_split_clause,[],[f487,f444,f267,f618]) ).

fof(f618,plain,
    ( spl17_74
  <=> function(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).

fof(f487,plain,
    ( function(sK4)
    | ~ spl17_12
    | ~ spl17_48 ),
    inference(resolution,[],[f445,f269]) ).

fof(f613,plain,
    spl17_73,
    inference(avatar_split_clause,[],[f173,f611]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f609,plain,
    spl17_72,
    inference(avatar_split_clause,[],[f172,f607]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f605,plain,
    spl17_71,
    inference(avatar_split_clause,[],[f171,f603]) ).

fof(f171,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f601,plain,
    spl17_70,
    inference(avatar_split_clause,[],[f154,f599]) ).

fof(f599,plain,
    ( spl17_70
  <=> ! [X0] :
        ( ~ empty(relation_rng(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).

fof(f154,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f69]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ empty(relation_rng(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_rng(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).

fof(f597,plain,
    spl17_69,
    inference(avatar_split_clause,[],[f153,f595]) ).

fof(f595,plain,
    ( spl17_69
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).

fof(f153,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f588,plain,
    spl17_68,
    inference(avatar_split_clause,[],[f167,f586]) ).

fof(f586,plain,
    ( spl17_68
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f584,plain,
    spl17_67,
    inference(avatar_split_clause,[],[f166,f582]) ).

fof(f582,plain,
    ( spl17_67
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f580,plain,
    spl17_66,
    inference(avatar_split_clause,[],[f155,f578]) ).

fof(f578,plain,
    ( spl17_66
  <=> ! [X0] :
        ( ordinal(X0)
        | ~ epsilon_connected(X0)
        | ~ epsilon_transitive(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).

fof(f155,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ epsilon_connected(X0)
      | ~ epsilon_transitive(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
     => ordinal(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).

fof(f566,plain,
    ( spl17_65
    | ~ spl17_3
    | ~ spl17_47 ),
    inference(avatar_split_clause,[],[f481,f440,f222,f563]) ).

fof(f563,plain,
    ( spl17_65
  <=> epsilon_connected(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).

fof(f481,plain,
    ( epsilon_connected(relation_dom(sK0))
    | ~ spl17_3
    | ~ spl17_47 ),
    inference(resolution,[],[f441,f224]) ).

fof(f546,plain,
    spl17_64,
    inference(avatar_split_clause,[],[f174,f544]) ).

fof(f544,plain,
    ( spl17_64
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f542,plain,
    spl17_63,
    inference(avatar_split_clause,[],[f165,f540]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( transfinite_sequence(X1)
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( transfinite_sequence(X1)
        & function(X1)
        & relation(X1) )
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( transfinite_sequence_of(X1,X0)
     => ( transfinite_sequence(X1)
        & function(X1)
        & relation(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).

fof(f538,plain,
    spl17_62,
    inference(avatar_split_clause,[],[f164,f536]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( function(X1)
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f534,plain,
    spl17_61,
    inference(avatar_split_clause,[],[f163,f532]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( relation(X1)
      | ~ transfinite_sequence_of(X1,X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f530,plain,
    spl17_60,
    inference(avatar_split_clause,[],[f152,f528]) ).

fof(f528,plain,
    ( spl17_60
  <=> ! [X0] :
        ( relation(relation_rng(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).

fof(f152,plain,
    ! [X0] :
      ( relation(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_rng(X0))
        & empty(relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

fof(f526,plain,
    spl17_59,
    inference(avatar_split_clause,[],[f151,f524]) ).

fof(f151,plain,
    ! [X0] :
      ( empty(relation_rng(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f66]) ).

fof(f522,plain,
    spl17_58,
    inference(avatar_split_clause,[],[f150,f520]) ).

fof(f520,plain,
    ( spl17_58
  <=> ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).

fof(f150,plain,
    ! [X0] :
      ( relation(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

fof(f518,plain,
    spl17_57,
    inference(avatar_split_clause,[],[f149,f516]) ).

fof(f149,plain,
    ! [X0] :
      ( empty(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f514,plain,
    spl17_56,
    inference(avatar_split_clause,[],[f145,f512]) ).

fof(f145,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f480,plain,
    ( spl17_55
    | ~ spl17_3
    | ~ spl17_46 ),
    inference(avatar_split_clause,[],[f471,f436,f222,f477]) ).

fof(f477,plain,
    ( spl17_55
  <=> epsilon_transitive(relation_dom(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).

fof(f471,plain,
    ( epsilon_transitive(relation_dom(sK0))
    | ~ spl17_3
    | ~ spl17_46 ),
    inference(resolution,[],[f437,f224]) ).

fof(f470,plain,
    spl17_54,
    inference(avatar_split_clause,[],[f161,f468]) ).

fof(f161,plain,
    ! [X0] : element(sK2(X0),X0),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0] : element(sK2(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f12,f94]) ).

fof(f94,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f12,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f466,plain,
    spl17_53,
    inference(avatar_split_clause,[],[f160,f464]) ).

fof(f160,plain,
    ! [X0] : transfinite_sequence_of(sK1(X0),X0),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0] : transfinite_sequence_of(sK1(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ? [X1] : transfinite_sequence_of(X1,X0)
     => transfinite_sequence_of(sK1(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f11,axiom,
    ! [X0] :
    ? [X1] : transfinite_sequence_of(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_ordinal1) ).

fof(f462,plain,
    spl17_52,
    inference(avatar_split_clause,[],[f148,f460]) ).

fof(f148,plain,
    ! [X0] :
      ( ordinal(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( empty(X0)
     => ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).

fof(f458,plain,
    spl17_51,
    inference(avatar_split_clause,[],[f147,f456]) ).

fof(f147,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f454,plain,
    spl17_50,
    inference(avatar_split_clause,[],[f146,f452]) ).

fof(f146,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f450,plain,
    spl17_49,
    inference(avatar_split_clause,[],[f144,f448]) ).

fof(f144,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f446,plain,
    spl17_48,
    inference(avatar_split_clause,[],[f143,f444]) ).

fof(f143,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] :
      ( empty(X0)
     => function(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

fof(f442,plain,
    spl17_47,
    inference(avatar_split_clause,[],[f142,f440]) ).

fof(f142,plain,
    ! [X0] :
      ( epsilon_connected(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ( epsilon_connected(X0)
        & epsilon_transitive(X0) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( epsilon_connected(X0)
        & epsilon_transitive(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).

fof(f438,plain,
    spl17_46,
    inference(avatar_split_clause,[],[f141,f436]) ).

fof(f141,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f434,plain,
    spl17_45,
    inference(avatar_split_clause,[],[f162,f432]) ).

fof(f162,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f430,plain,
    spl17_44,
    inference(avatar_split_clause,[],[f210,f427]) ).

fof(f427,plain,
    ( spl17_44
  <=> function(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).

fof(f210,plain,
    function(sK16),
    inference(cnf_transformation,[],[f125]) ).

fof(f125,plain,
    ( function(sK16)
    & empty(sK16)
    & relation(sK16) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f26,f124]) ).

fof(f124,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK16)
      & empty(sK16)
      & relation(sK16) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(f425,plain,
    spl17_43,
    inference(avatar_split_clause,[],[f209,f422]) ).

fof(f209,plain,
    empty(sK16),
    inference(cnf_transformation,[],[f125]) ).

fof(f420,plain,
    spl17_42,
    inference(avatar_split_clause,[],[f208,f417]) ).

fof(f417,plain,
    ( spl17_42
  <=> relation(sK16) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).

fof(f208,plain,
    relation(sK16),
    inference(cnf_transformation,[],[f125]) ).

fof(f415,plain,
    spl17_41,
    inference(avatar_split_clause,[],[f207,f412]) ).

fof(f412,plain,
    ( spl17_41
  <=> ordinal(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).

fof(f207,plain,
    ordinal(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f123,plain,
    ( ordinal(sK15)
    & epsilon_connected(sK15)
    & epsilon_transitive(sK15)
    & empty(sK15)
    & function(sK15)
    & relation(sK15) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f55,f122]) ).

fof(f122,plain,
    ( ? [X0] :
        ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0)
        & empty(X0)
        & function(X0)
        & relation(X0) )
   => ( ordinal(sK15)
      & epsilon_connected(sK15)
      & epsilon_transitive(sK15)
      & empty(sK15)
      & function(sK15)
      & relation(sK15) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ? [X0] :
      ( ordinal(X0)
      & epsilon_connected(X0)
      & epsilon_transitive(X0)
      & empty(X0)
      & function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f27]) ).

fof(f27,axiom,
    ? [X0] :
      ( ordinal(X0)
      & epsilon_connected(X0)
      & epsilon_transitive(X0)
      & empty(X0)
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).

fof(f410,plain,
    spl17_40,
    inference(avatar_split_clause,[],[f206,f407]) ).

fof(f407,plain,
    ( spl17_40
  <=> epsilon_connected(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).

fof(f206,plain,
    epsilon_connected(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f405,plain,
    spl17_39,
    inference(avatar_split_clause,[],[f205,f402]) ).

fof(f402,plain,
    ( spl17_39
  <=> epsilon_transitive(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).

fof(f205,plain,
    epsilon_transitive(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f400,plain,
    spl17_38,
    inference(avatar_split_clause,[],[f204,f397]) ).

fof(f204,plain,
    empty(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f395,plain,
    spl17_37,
    inference(avatar_split_clause,[],[f203,f392]) ).

fof(f392,plain,
    ( spl17_37
  <=> function(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).

fof(f203,plain,
    function(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f390,plain,
    spl17_36,
    inference(avatar_split_clause,[],[f202,f387]) ).

fof(f387,plain,
    ( spl17_36
  <=> relation(sK15) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).

fof(f202,plain,
    relation(sK15),
    inference(cnf_transformation,[],[f123]) ).

fof(f385,plain,
    spl17_35,
    inference(avatar_split_clause,[],[f201,f382]) ).

fof(f382,plain,
    ( spl17_35
  <=> function(sK14) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).

fof(f201,plain,
    function(sK14),
    inference(cnf_transformation,[],[f121]) ).

fof(f121,plain,
    ( function(sK14)
    & relation(sK14) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f57,f120]) ).

fof(f120,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK14)
      & relation(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f57,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f30]) ).

fof(f30,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

fof(f380,plain,
    spl17_34,
    inference(avatar_split_clause,[],[f200,f377]) ).

fof(f377,plain,
    ( spl17_34
  <=> relation(sK14) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).

fof(f200,plain,
    relation(sK14),
    inference(cnf_transformation,[],[f121]) ).

fof(f375,plain,
    spl17_33,
    inference(avatar_split_clause,[],[f199,f372]) ).

fof(f372,plain,
    ( spl17_33
  <=> transfinite_sequence(sK13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).

fof(f199,plain,
    transfinite_sequence(sK13),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ( transfinite_sequence(sK13)
    & function(sK13)
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f34,f118]) ).

fof(f118,plain,
    ( ? [X0] :
        ( transfinite_sequence(X0)
        & function(X0)
        & relation(X0) )
   => ( transfinite_sequence(sK13)
      & function(sK13)
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,axiom,
    ? [X0] :
      ( transfinite_sequence(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).

fof(f370,plain,
    spl17_32,
    inference(avatar_split_clause,[],[f198,f367]) ).

fof(f367,plain,
    ( spl17_32
  <=> function(sK13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).

fof(f198,plain,
    function(sK13),
    inference(cnf_transformation,[],[f119]) ).

fof(f365,plain,
    spl17_31,
    inference(avatar_split_clause,[],[f197,f362]) ).

fof(f362,plain,
    ( spl17_31
  <=> relation(sK13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).

fof(f197,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f119]) ).

fof(f360,plain,
    spl17_30,
    inference(avatar_split_clause,[],[f196,f357]) ).

fof(f357,plain,
    ( spl17_30
  <=> function(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).

fof(f196,plain,
    function(sK12),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ( function(sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f22,f116]) ).

fof(f116,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(f355,plain,
    spl17_29,
    inference(avatar_split_clause,[],[f195,f352]) ).

fof(f352,plain,
    ( spl17_29
  <=> relation(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).

fof(f195,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f117]) ).

fof(f350,plain,
    spl17_28,
    inference(avatar_split_clause,[],[f194,f347]) ).

fof(f347,plain,
    ( spl17_28
  <=> function(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).

fof(f194,plain,
    function(sK11),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ( function(sK11)
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f53,f114]) ).

fof(f114,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f33]) ).

fof(f33,axiom,
    ? [X0] :
      ( function(X0)
      & relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).

fof(f345,plain,
    spl17_27,
    inference(avatar_split_clause,[],[f193,f342]) ).

fof(f342,plain,
    ( spl17_27
  <=> relation(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).

fof(f193,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f115]) ).

fof(f340,plain,
    spl17_26,
    inference(avatar_split_clause,[],[f192,f337]) ).

fof(f337,plain,
    ( spl17_26
  <=> relation(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).

fof(f192,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    relation(sK10),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f51,f112]) ).

fof(f112,plain,
    ( ? [X0] : relation(X0)
   => relation(sK10) ),
    introduced(choice_axiom,[]) ).

fof(f51,plain,
    ? [X0] : relation(X0),
    inference(pure_predicate_removal,[],[f32]) ).

fof(f32,axiom,
    ? [X0] :
      ( relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).

fof(f335,plain,
    spl17_25,
    inference(avatar_split_clause,[],[f191,f332]) ).

fof(f332,plain,
    ( spl17_25
  <=> function(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).

fof(f191,plain,
    function(sK9),
    inference(cnf_transformation,[],[f111]) ).

fof(f111,plain,
    ( function(sK9)
    & relation(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f49,f110]) ).

fof(f110,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK9)
      & relation(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f35]) ).

fof(f35,axiom,
    ? [X0] :
      ( function(X0)
      & relation_non_empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).

fof(f330,plain,
    spl17_24,
    inference(avatar_split_clause,[],[f190,f327]) ).

fof(f327,plain,
    ( spl17_24
  <=> relation(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).

fof(f190,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f111]) ).

fof(f325,plain,
    spl17_23,
    inference(avatar_split_clause,[],[f189,f322]) ).

fof(f322,plain,
    ( spl17_23
  <=> relation(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).

fof(f189,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ( relation(sK8)
    & empty(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f24,f108]) ).

fof(f108,plain,
    ( ? [X0] :
        ( relation(X0)
        & empty(X0) )
   => ( relation(sK8)
      & empty(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,axiom,
    ? [X0] :
      ( relation(X0)
      & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(f320,plain,
    spl17_22,
    inference(avatar_split_clause,[],[f188,f317]) ).

fof(f188,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f109]) ).

fof(f315,plain,
    spl17_21,
    inference(avatar_split_clause,[],[f187,f312]) ).

fof(f312,plain,
    ( spl17_21
  <=> ordinal(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).

fof(f187,plain,
    ordinal(sK7),
    inference(cnf_transformation,[],[f107]) ).

fof(f107,plain,
    ( ordinal(sK7)
    & epsilon_connected(sK7)
    & epsilon_transitive(sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f23,f106]) ).

fof(f106,plain,
    ( ? [X0] :
        ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0) )
   => ( ordinal(sK7)
      & epsilon_connected(sK7)
      & epsilon_transitive(sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,axiom,
    ? [X0] :
      ( ordinal(X0)
      & epsilon_connected(X0)
      & epsilon_transitive(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).

fof(f310,plain,
    spl17_20,
    inference(avatar_split_clause,[],[f186,f307]) ).

fof(f307,plain,
    ( spl17_20
  <=> epsilon_connected(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).

fof(f186,plain,
    epsilon_connected(sK7),
    inference(cnf_transformation,[],[f107]) ).

fof(f305,plain,
    spl17_19,
    inference(avatar_split_clause,[],[f185,f302]) ).

fof(f302,plain,
    ( spl17_19
  <=> epsilon_transitive(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).

fof(f185,plain,
    epsilon_transitive(sK7),
    inference(cnf_transformation,[],[f107]) ).

fof(f300,plain,
    spl17_18,
    inference(avatar_split_clause,[],[f184,f297]) ).

fof(f297,plain,
    ( spl17_18
  <=> relation(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).

fof(f184,plain,
    relation(sK6),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ( relation(sK6)
    & ~ empty(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f28,f104]) ).

fof(f104,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ empty(X0) )
   => ( relation(sK6)
      & ~ empty(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f28,axiom,
    ? [X0] :
      ( relation(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

fof(f295,plain,
    ~ spl17_17,
    inference(avatar_split_clause,[],[f183,f292]) ).

fof(f292,plain,
    ( spl17_17
  <=> empty(sK6) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).

fof(f183,plain,
    ~ empty(sK6),
    inference(cnf_transformation,[],[f105]) ).

fof(f290,plain,
    spl17_16,
    inference(avatar_split_clause,[],[f182,f287]) ).

fof(f287,plain,
    ( spl17_16
  <=> ordinal(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).

fof(f182,plain,
    ordinal(sK5),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ( ordinal(sK5)
    & epsilon_connected(sK5)
    & epsilon_transitive(sK5)
    & ~ empty(sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f31,f102]) ).

fof(f102,plain,
    ( ? [X0] :
        ( ordinal(X0)
        & epsilon_connected(X0)
        & epsilon_transitive(X0)
        & ~ empty(X0) )
   => ( ordinal(sK5)
      & epsilon_connected(sK5)
      & epsilon_transitive(sK5)
      & ~ empty(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,axiom,
    ? [X0] :
      ( ordinal(X0)
      & epsilon_connected(X0)
      & epsilon_transitive(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).

fof(f285,plain,
    spl17_15,
    inference(avatar_split_clause,[],[f181,f282]) ).

fof(f282,plain,
    ( spl17_15
  <=> epsilon_connected(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).

fof(f181,plain,
    epsilon_connected(sK5),
    inference(cnf_transformation,[],[f103]) ).

fof(f280,plain,
    spl17_14,
    inference(avatar_split_clause,[],[f180,f277]) ).

fof(f277,plain,
    ( spl17_14
  <=> epsilon_transitive(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).

fof(f180,plain,
    epsilon_transitive(sK5),
    inference(cnf_transformation,[],[f103]) ).

fof(f275,plain,
    ~ spl17_13,
    inference(avatar_split_clause,[],[f179,f272]) ).

fof(f272,plain,
    ( spl17_13
  <=> empty(sK5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).

fof(f179,plain,
    ~ empty(sK5),
    inference(cnf_transformation,[],[f103]) ).

fof(f270,plain,
    spl17_12,
    inference(avatar_split_clause,[],[f178,f267]) ).

fof(f178,plain,
    empty(sK4),
    inference(cnf_transformation,[],[f101]) ).

fof(f101,plain,
    empty(sK4),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f100]) ).

fof(f100,plain,
    ( ? [X0] : empty(X0)
   => empty(sK4) ),
    introduced(choice_axiom,[]) ).

fof(f25,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f265,plain,
    ~ spl17_11,
    inference(avatar_split_clause,[],[f177,f262]) ).

fof(f262,plain,
    ( spl17_11
  <=> empty(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).

fof(f177,plain,
    ~ empty(sK3),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ~ empty(sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f29,f98]) ).

fof(f98,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f29,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f260,plain,
    spl17_10,
    inference(avatar_split_clause,[],[f140,f257]) ).

fof(f257,plain,
    ( spl17_10
  <=> ordinal(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).

fof(f140,plain,
    ordinal(empty_set),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & function(empty_set)
    & relation(empty_set) ),
    inference(pure_predicate_removal,[],[f50]) ).

fof(f50,plain,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & one_to_one(empty_set)
    & function(empty_set)
    & relation(empty_set) ),
    inference(pure_predicate_removal,[],[f15]) ).

fof(f15,axiom,
    ( ordinal(empty_set)
    & epsilon_connected(empty_set)
    & epsilon_transitive(empty_set)
    & empty(empty_set)
    & one_to_one(empty_set)
    & function(empty_set)
    & relation_empty_yielding(empty_set)
    & relation(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).

fof(f255,plain,
    spl17_9,
    inference(avatar_split_clause,[],[f139,f252]) ).

fof(f252,plain,
    ( spl17_9
  <=> epsilon_connected(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).

fof(f139,plain,
    epsilon_connected(empty_set),
    inference(cnf_transformation,[],[f54]) ).

fof(f250,plain,
    spl17_8,
    inference(avatar_split_clause,[],[f138,f247]) ).

fof(f247,plain,
    ( spl17_8
  <=> epsilon_transitive(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).

fof(f138,plain,
    epsilon_transitive(empty_set),
    inference(cnf_transformation,[],[f54]) ).

fof(f245,plain,
    spl17_7,
    inference(avatar_split_clause,[],[f136,f242]) ).

fof(f242,plain,
    ( spl17_7
  <=> function(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).

fof(f136,plain,
    function(empty_set),
    inference(cnf_transformation,[],[f54]) ).

fof(f240,plain,
    spl17_6,
    inference(avatar_split_clause,[],[f132,f237]) ).

fof(f237,plain,
    ( spl17_6
  <=> relation(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).

fof(f132,plain,
    relation(empty_set),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f235,plain,
    spl17_5,
    inference(avatar_split_clause,[],[f130,f232]) ).

fof(f130,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f230,plain,
    ~ spl17_4,
    inference(avatar_split_clause,[],[f129,f227]) ).

fof(f129,plain,
    ~ transfinite_sequence_of(sK0,relation_rng(sK0)),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
    & ordinal(relation_dom(sK0))
    & function(sK0)
    & relation(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f59,f89]) ).

fof(f89,plain,
    ( ? [X0] :
        ( ~ transfinite_sequence_of(X0,relation_rng(X0))
        & ordinal(relation_dom(X0))
        & function(X0)
        & relation(X0) )
   => ( ~ transfinite_sequence_of(sK0,relation_rng(sK0))
      & ordinal(relation_dom(sK0))
      & function(sK0)
      & relation(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f59,plain,
    ? [X0] :
      ( ~ transfinite_sequence_of(X0,relation_rng(X0))
      & ordinal(relation_dom(X0))
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ? [X0] :
      ( ~ transfinite_sequence_of(X0,relation_rng(X0))
      & ordinal(relation_dom(X0))
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( ordinal(relation_dom(X0))
         => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    inference(negated_conjecture,[],[f40]) ).

fof(f40,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( ordinal(relation_dom(X0))
       => transfinite_sequence_of(X0,relation_rng(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_ordinal1) ).

fof(f225,plain,
    spl17_3,
    inference(avatar_split_clause,[],[f128,f222]) ).

fof(f128,plain,
    ordinal(relation_dom(sK0)),
    inference(cnf_transformation,[],[f90]) ).

fof(f220,plain,
    spl17_2,
    inference(avatar_split_clause,[],[f127,f217]) ).

fof(f127,plain,
    function(sK0),
    inference(cnf_transformation,[],[f90]) ).

fof(f215,plain,
    spl17_1,
    inference(avatar_split_clause,[],[f126,f212]) ).

fof(f126,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem    : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.08  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27  % Computer : n016.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit   : 300
% 0.07/0.27  % WCLimit    : 300
% 0.07/0.27  % DateTime   : Mon Apr 29 23:57:25 EDT 2024
% 0.07/0.27  % CPUTime    : 
% 0.07/0.27  % (6054)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28  % (6055)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.29  TRYING [1]
% 0.07/0.29  TRYING [2]
% 0.07/0.29  % (6057)WARNING: value z3 for option sas not known
% 0.07/0.29  % (6056)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.29  % (6058)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.29  % (6059)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)
% 0.07/0.29  % (6060)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)
% 0.07/0.29  % (6057)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)
% 0.07/0.29  % (6061)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)
% 0.07/0.29  TRYING [3]
% 0.07/0.29  TRYING [1]
% 0.07/0.29  TRYING [2]
% 0.07/0.29  TRYING [3]
% 0.07/0.30  TRYING [4]
% 0.07/0.30  TRYING [4]
% 0.07/0.30  TRYING [1]
% 0.07/0.30  TRYING [2]
% 0.07/0.30  TRYING [3]
% 0.07/0.30  % (6059)First to succeed.
% 0.07/0.30  TRYING [5]
% 0.07/0.30  TRYING [4]
% 0.12/0.31  % (6059)Refutation found. Thanks to Tanya!
% 0.12/0.31  % SZS status Theorem for theBenchmark
% 0.12/0.31  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.31  % (6059)------------------------------
% 0.12/0.31  % (6059)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.12/0.31  % (6059)Termination reason: Refutation
% 0.12/0.31  
% 0.12/0.31  % (6059)Memory used [KB]: 1087
% 0.12/0.31  % (6059)Time elapsed: 0.016 s
% 0.12/0.31  % (6059)Instructions burned: 25 (million)
% 0.12/0.31  % (6059)------------------------------
% 0.12/0.31  % (6059)------------------------------
% 0.12/0.31  % (6054)Success in time 0.033 s
%------------------------------------------------------------------------------