TSTP Solution File: SEU236+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n031.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 : Wed May  1 03:51:02 EDT 2024

% Result   : Theorem 1.06s 0.89s
% Output   : Refutation 1.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   96 (  10 unt;   0 def)
%            Number of atoms       :  328 (  31 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  371 ( 139   ~; 142   |;  59   &)
%                                         (  15 <=>;  15  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   5 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :  118 (  99   !;  19   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f591,plain,
    $false,
    inference(avatar_sat_refutation,[],[f256,f257,f348,f351,f372,f375,f590]) ).

fof(f590,plain,
    ( ~ spl18_1
    | spl18_6 ),
    inference(avatar_contradiction_clause,[],[f589]) ).

fof(f589,plain,
    ( $false
    | ~ spl18_1
    | spl18_6 ),
    inference(subsumption_resolution,[],[f588,f578]) ).

fof(f578,plain,
    ( ~ subset(singleton(sK0),sK1)
    | ~ spl18_1
    | spl18_6 ),
    inference(subsumption_resolution,[],[f570,f380]) ).

fof(f380,plain,
    ( subset(sK0,sK1)
    | ~ spl18_1 ),
    inference(subsumption_resolution,[],[f376,f291]) ).

fof(f291,plain,
    epsilon_transitive(sK1),
    inference(resolution,[],[f185,f144]) ).

fof(f144,plain,
    ordinal(sK1),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ( ( ~ ordinal_subset(succ(sK0),sK1)
      | ~ in(sK0,sK1) )
    & ( ordinal_subset(succ(sK0),sK1)
      | in(sK0,sK1) )
    & ordinal(sK1)
    & ordinal(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f99,f101,f100]) ).

fof(f100,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ ordinal_subset(succ(X0),X1)
              | ~ in(X0,X1) )
            & ( ordinal_subset(succ(X0),X1)
              | in(X0,X1) )
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ( ~ ordinal_subset(succ(sK0),X1)
            | ~ in(sK0,X1) )
          & ( ordinal_subset(succ(sK0),X1)
            | in(sK0,X1) )
          & ordinal(X1) )
      & ordinal(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ( ? [X1] :
        ( ( ~ ordinal_subset(succ(sK0),X1)
          | ~ in(sK0,X1) )
        & ( ordinal_subset(succ(sK0),X1)
          | in(sK0,X1) )
        & ordinal(X1) )
   => ( ( ~ ordinal_subset(succ(sK0),sK1)
        | ~ in(sK0,sK1) )
      & ( ordinal_subset(succ(sK0),sK1)
        | in(sK0,sK1) )
      & ordinal(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(succ(X0),X1)
            | ~ in(X0,X1) )
          & ( ordinal_subset(succ(X0),X1)
            | in(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( in(X0,X1)
          <~> ordinal_subset(succ(X0),X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ( in(X0,X1)
            <=> ordinal_subset(succ(X0),X1) ) ) ),
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ( in(X0,X1)
          <=> ordinal_subset(succ(X0),X1) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',t33_ordinal1) ).

fof(f185,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,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/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',cc1_ordinal1) ).

fof(f376,plain,
    ( subset(sK0,sK1)
    | ~ epsilon_transitive(sK1)
    | ~ spl18_1 ),
    inference(resolution,[],[f250,f206]) ).

fof(f206,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | subset(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f126]) ).

fof(f126,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK9(X0),X0)
          & in(sK9(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f124,f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK9(X0),X0)
        & in(sK9(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f123]) ).

fof(f123,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X1] :
            ( subset(X1,X0)
            | ~ in(X1,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',d2_ordinal1) ).

fof(f250,plain,
    ( in(sK0,sK1)
    | ~ spl18_1 ),
    inference(avatar_component_clause,[],[f249]) ).

fof(f249,plain,
    ( spl18_1
  <=> in(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).

fof(f570,plain,
    ( ~ subset(singleton(sK0),sK1)
    | ~ subset(sK0,sK1)
    | spl18_6 ),
    inference(resolution,[],[f196,f346]) ).

fof(f346,plain,
    ( ~ subset(set_union2(sK0,singleton(sK0)),sK1)
    | spl18_6 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f345,plain,
    ( spl18_6
  <=> subset(set_union2(sK0,singleton(sK0)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).

fof(f196,plain,
    ! [X2,X0,X1] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( subset(set_union2(X0,X2),X1)
      | ~ subset(X2,X1)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X2,X1)
        & subset(X0,X1) )
     => subset(set_union2(X0,X2),X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',t8_xboole_1) ).

fof(f588,plain,
    ( subset(singleton(sK0),sK1)
    | ~ spl18_1
    | spl18_6 ),
    inference(subsumption_resolution,[],[f586,f250]) ).

fof(f586,plain,
    ( ~ in(sK0,sK1)
    | subset(singleton(sK0),sK1)
    | ~ spl18_1
    | spl18_6 ),
    inference(superposition,[],[f205,f579]) ).

fof(f579,plain,
    ( sK0 = sK8(singleton(sK0),sK1)
    | ~ spl18_1
    | spl18_6 ),
    inference(resolution,[],[f578,f327]) ).

fof(f327,plain,
    ! [X0,X1] :
      ( subset(singleton(X0),X1)
      | sK8(singleton(X0),X1) = X0 ),
    inference(resolution,[],[f204,f247]) ).

fof(f247,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f191]) ).

fof(f191,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK7(X0,X1) != X0
            | ~ in(sK7(X0,X1),X1) )
          & ( sK7(X0,X1) = X0
            | in(sK7(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f115,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK7(X0,X1) != X0
          | ~ in(sK7(X0,X1),X1) )
        & ( sK7(X0,X1) = X0
          | in(sK7(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f114]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) )
      & ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',d1_tarski) ).

fof(f204,plain,
    ! [X0,X1] :
      ( in(sK8(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK8(X0,X1),X1)
          & in(sK8(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f120,f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK8(X0,X1),X1)
        & in(sK8(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f119]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',d3_tarski) ).

fof(f205,plain,
    ! [X0,X1] :
      ( ~ in(sK8(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f375,plain,
    ( spl18_2
    | ~ spl18_5
    | ~ spl18_6 ),
    inference(avatar_split_clause,[],[f374,f345,f341,f253]) ).

fof(f253,plain,
    ( spl18_2
  <=> ordinal_subset(set_union2(sK0,singleton(sK0)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).

fof(f341,plain,
    ( spl18_5
  <=> ordinal(set_union2(sK0,singleton(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).

fof(f374,plain,
    ( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ spl18_5
    | ~ spl18_6 ),
    inference(subsumption_resolution,[],[f373,f342]) ).

fof(f342,plain,
    ( ordinal(set_union2(sK0,singleton(sK0)))
    | ~ spl18_5 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f373,plain,
    ( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ ordinal(set_union2(sK0,singleton(sK0)))
    | ~ spl18_6 ),
    inference(subsumption_resolution,[],[f364,f144]) ).

fof(f364,plain,
    ( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ ordinal(sK1)
    | ~ ordinal(set_union2(sK0,singleton(sK0)))
    | ~ spl18_6 ),
    inference(resolution,[],[f347,f158]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ordinal_subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',redefinition_r1_ordinal1) ).

fof(f347,plain,
    ( subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ spl18_6 ),
    inference(avatar_component_clause,[],[f345]) ).

fof(f372,plain,
    ( spl18_1
    | ~ spl18_6 ),
    inference(avatar_split_clause,[],[f366,f345,f249]) ).

fof(f366,plain,
    ( in(sK0,sK1)
    | ~ spl18_6 ),
    inference(resolution,[],[f365,f239]) ).

fof(f239,plain,
    ! [X0] : in(X0,set_union2(X0,singleton(X0))),
    inference(definition_unfolding,[],[f149,f155]) ).

fof(f155,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',d1_ordinal1) ).

fof(f149,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',t10_ordinal1) ).

fof(f365,plain,
    ( ! [X0] :
        ( ~ in(X0,set_union2(sK0,singleton(sK0)))
        | in(X0,sK1) )
    | ~ spl18_6 ),
    inference(resolution,[],[f347,f203]) ).

fof(f203,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f122]) ).

fof(f351,plain,
    spl18_5,
    inference(avatar_contradiction_clause,[],[f350]) ).

fof(f350,plain,
    ( $false
    | spl18_5 ),
    inference(subsumption_resolution,[],[f349,f143]) ).

fof(f143,plain,
    ordinal(sK0),
    inference(cnf_transformation,[],[f102]) ).

fof(f349,plain,
    ( ~ ordinal(sK0)
    | spl18_5 ),
    inference(resolution,[],[f343,f240]) ).

fof(f240,plain,
    ! [X0] :
      ( ordinal(set_union2(X0,singleton(X0)))
      | ~ ordinal(X0) ),
    inference(definition_unfolding,[],[f153,f155]) ).

fof(f153,plain,
    ! [X0] :
      ( ordinal(succ(X0))
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0] :
      ( ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ( ordinal(succ(X0))
        & epsilon_connected(succ(X0))
        & epsilon_transitive(succ(X0))
        & ~ empty(succ(X0)) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806',fc3_ordinal1) ).

fof(f343,plain,
    ( ~ ordinal(set_union2(sK0,singleton(sK0)))
    | spl18_5 ),
    inference(avatar_component_clause,[],[f341]) ).

fof(f348,plain,
    ( ~ spl18_5
    | spl18_6
    | ~ spl18_2 ),
    inference(avatar_split_clause,[],[f339,f253,f345,f341]) ).

fof(f339,plain,
    ( subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ ordinal(set_union2(sK0,singleton(sK0)))
    | ~ spl18_2 ),
    inference(subsumption_resolution,[],[f336,f144]) ).

fof(f336,plain,
    ( subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ ordinal(sK1)
    | ~ ordinal(set_union2(sK0,singleton(sK0)))
    | ~ spl18_2 ),
    inference(resolution,[],[f157,f254]) ).

fof(f254,plain,
    ( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ spl18_2 ),
    inference(avatar_component_clause,[],[f253]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ~ ordinal_subset(X0,X1)
      | subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f103]) ).

fof(f257,plain,
    ( spl18_1
    | spl18_2 ),
    inference(avatar_split_clause,[],[f238,f253,f249]) ).

fof(f238,plain,
    ( ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | in(sK0,sK1) ),
    inference(definition_unfolding,[],[f145,f155]) ).

fof(f145,plain,
    ( ordinal_subset(succ(sK0),sK1)
    | in(sK0,sK1) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f256,plain,
    ( ~ spl18_1
    | ~ spl18_2 ),
    inference(avatar_split_clause,[],[f237,f253,f249]) ).

fof(f237,plain,
    ( ~ ordinal_subset(set_union2(sK0,singleton(sK0)),sK1)
    | ~ in(sK0,sK1) ),
    inference(definition_unfolding,[],[f146,f155]) ).

fof(f146,plain,
    ( ~ ordinal_subset(succ(sK0),sK1)
    | ~ in(sK0,sK1) ),
    inference(cnf_transformation,[],[f102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU236+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35  % Computer : n031.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Apr 30 16:45:14 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.rcn0TgKsHu/Vampire---4.8_11806
% 0.56/0.78  % (12016)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2995ds/51Mi)
% 0.56/0.78  % (12022)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2995ds/56Mi)
% 0.56/0.78  % (12015)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2995ds/34Mi)
% 0.56/0.78  % (12017)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2995ds/78Mi)
% 0.56/0.78  % (12020)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/45Mi)
% 0.56/0.78  % (12019)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2995ds/34Mi)
% 0.56/0.78  % (12018)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2995ds/33Mi)
% 0.56/0.78  % (12021)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2995ds/83Mi)
% 0.56/0.78  % (12022)Refutation not found, incomplete strategy% (12022)------------------------------
% 0.56/0.78  % (12022)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.78  % (12022)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.78  
% 0.56/0.78  % (12022)Memory used [KB]: 1063
% 0.56/0.78  % (12022)Time elapsed: 0.003 s
% 0.56/0.78  % (12022)Instructions burned: 3 (million)
% 0.56/0.78  % (12022)------------------------------
% 0.56/0.78  % (12022)------------------------------
% 0.56/0.79  % (12020)Refutation not found, incomplete strategy% (12020)------------------------------
% 0.56/0.79  % (12020)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.79  % (12020)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.79  
% 0.56/0.79  % (12020)Memory used [KB]: 1051
% 0.56/0.79  % (12020)Time elapsed: 0.006 s
% 0.56/0.79  % (12020)Instructions burned: 3 (million)
% 0.56/0.79  % (12020)------------------------------
% 0.56/0.79  % (12020)------------------------------
% 0.56/0.79  % (12023)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.63/0.79  % (12024)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.63/0.81  % (12018)Instruction limit reached!
% 0.63/0.81  % (12018)------------------------------
% 0.63/0.81  % (12018)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.81  % (12018)Termination reason: Unknown
% 0.63/0.81  % (12018)Termination phase: Saturation
% 0.63/0.81  
% 0.63/0.81  % (12018)Memory used [KB]: 1275
% 0.63/0.81  % (12018)Time elapsed: 0.031 s
% 0.63/0.81  % (12018)Instructions burned: 33 (million)
% 0.63/0.81  % (12018)------------------------------
% 0.63/0.81  % (12018)------------------------------
% 0.63/0.81  % (12016)Instruction limit reached!
% 0.63/0.81  % (12016)------------------------------
% 0.63/0.81  % (12016)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.81  % (12016)Termination reason: Unknown
% 0.63/0.81  % (12016)Termination phase: Saturation
% 0.63/0.81  
% 0.63/0.81  % (12016)Memory used [KB]: 1649
% 0.63/0.81  % (12016)Time elapsed: 0.035 s
% 0.63/0.81  % (12016)Instructions burned: 52 (million)
% 0.63/0.81  % (12016)------------------------------
% 0.63/0.81  % (12016)------------------------------
% 0.63/0.81  % (12023)Instruction limit reached!
% 0.63/0.81  % (12023)------------------------------
% 0.63/0.81  % (12023)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.81  % (12023)Termination reason: Unknown
% 0.63/0.81  % (12023)Termination phase: Saturation
% 0.63/0.82  
% 0.63/0.82  % (12023)Memory used [KB]: 1832
% 0.63/0.82  % (12023)Time elapsed: 0.029 s
% 0.63/0.82  % (12023)Instructions burned: 56 (million)
% 0.63/0.82  % (12023)------------------------------
% 0.63/0.82  % (12023)------------------------------
% 0.63/0.82  % (12029)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.63/0.82  % (12015)Instruction limit reached!
% 0.63/0.82  % (12015)------------------------------
% 0.63/0.82  % (12015)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.82  % (12015)Termination reason: Unknown
% 0.63/0.82  % (12015)Termination phase: Saturation
% 0.63/0.82  
% 0.63/0.82  % (12015)Memory used [KB]: 1415
% 0.63/0.82  % (12015)Time elapsed: 0.038 s
% 0.63/0.82  % (12015)Instructions burned: 34 (million)
% 0.63/0.82  % (12015)------------------------------
% 0.63/0.82  % (12015)------------------------------
% 0.63/0.82  % (12019)Instruction limit reached!
% 0.63/0.82  % (12019)------------------------------
% 0.63/0.82  % (12019)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.82  % (12019)Termination reason: Unknown
% 0.63/0.82  % (12019)Termination phase: Saturation
% 0.63/0.82  
% 0.63/0.82  % (12019)Memory used [KB]: 1550
% 0.63/0.82  % (12019)Time elapsed: 0.038 s
% 0.63/0.82  % (12019)Instructions burned: 34 (million)
% 0.63/0.82  % (12019)------------------------------
% 0.63/0.82  % (12019)------------------------------
% 0.63/0.82  % (12030)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.63/0.82  % (12028)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.63/0.82  % (12031)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.63/0.82  % (12032)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.63/0.83  % (12031)Refutation not found, incomplete strategy% (12031)------------------------------
% 0.63/0.83  % (12031)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.83  % (12031)Termination reason: Refutation not found, incomplete strategy
% 0.63/0.83  
% 0.63/0.83  % (12031)Memory used [KB]: 1136
% 0.63/0.83  % (12031)Time elapsed: 0.004 s
% 0.63/0.83  % (12031)Instructions burned: 5 (million)
% 0.63/0.83  % (12031)------------------------------
% 0.63/0.83  % (12031)------------------------------
% 0.63/0.83  % (12033)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.63/0.84  % (12024)Instruction limit reached!
% 0.63/0.84  % (12024)------------------------------
% 0.63/0.84  % (12024)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.84  % (12024)Termination reason: Unknown
% 0.63/0.84  % (12024)Termination phase: Saturation
% 0.63/0.84  
% 0.63/0.84  % (12024)Memory used [KB]: 1523
% 0.63/0.84  % (12024)Time elapsed: 0.045 s
% 0.63/0.84  % (12024)Instructions burned: 51 (million)
% 0.63/0.84  % (12024)------------------------------
% 0.63/0.84  % (12024)------------------------------
% 0.63/0.84  % (12037)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on Vampire---4 for (2995ds/143Mi)
% 0.63/0.85  % (12017)Instruction limit reached!
% 0.63/0.85  % (12017)------------------------------
% 0.63/0.85  % (12017)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.85  % (12017)Termination reason: Unknown
% 0.63/0.85  % (12017)Termination phase: Saturation
% 0.63/0.85  
% 0.63/0.85  % (12017)Memory used [KB]: 2077
% 0.63/0.85  % (12017)Time elapsed: 0.068 s
% 0.63/0.85  % (12017)Instructions burned: 79 (million)
% 0.63/0.85  % (12017)------------------------------
% 0.63/0.85  % (12017)------------------------------
% 0.63/0.85  % (12029)Instruction limit reached!
% 0.63/0.85  % (12029)------------------------------
% 0.63/0.85  % (12029)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.85  % (12029)Termination reason: Unknown
% 0.63/0.85  % (12029)Termination phase: Saturation
% 0.63/0.85  
% 0.63/0.85  % (12029)Memory used [KB]: 1612
% 0.63/0.85  % (12029)Time elapsed: 0.054 s
% 0.63/0.85  % (12029)Instructions burned: 53 (million)
% 0.63/0.85  % (12029)------------------------------
% 0.63/0.85  % (12029)------------------------------
% 0.63/0.85  % (12021)Instruction limit reached!
% 0.63/0.85  % (12021)------------------------------
% 0.63/0.85  % (12021)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.63/0.85  % (12021)Termination reason: Unknown
% 0.63/0.85  % (12021)Termination phase: Saturation
% 0.63/0.85  
% 0.63/0.85  % (12021)Memory used [KB]: 2528
% 0.63/0.85  % (12021)Time elapsed: 0.069 s
% 0.63/0.85  % (12021)Instructions burned: 84 (million)
% 0.63/0.85  % (12021)------------------------------
% 0.63/0.85  % (12021)------------------------------
% 0.63/0.85  % (12040)lrs+1666_1:1_sil=4000:sp=occurrence:sos=on:urr=on:newcnf=on:i=62:amm=off:ep=R:erd=off:nm=0:plsq=on:plsqr=14,1_0 on Vampire---4 for (2995ds/62Mi)
% 0.63/0.85  % (12039)lrs+1011_1:2_to=lpo:sil=8000:plsqc=1:plsq=on:plsqr=326,59:sp=weighted_frequency:plsql=on:nwc=10.0:newcnf=on:i=93:awrs=converge:awrsf=200:bd=off:ins=1:rawr=on:alpa=false:avsq=on:avsqr=1,16_0 on Vampire---4 for (2995ds/93Mi)
% 0.63/0.85  % (12041)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=32:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on Vampire---4 for (2995ds/32Mi)
% 1.04/0.87  % (12041)Instruction limit reached!
% 1.04/0.87  % (12041)------------------------------
% 1.04/0.87  % (12041)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.04/0.87  % (12041)Termination reason: Unknown
% 1.04/0.87  % (12041)Termination phase: Saturation
% 1.04/0.87  
% 1.04/0.87  % (12041)Memory used [KB]: 1416
% 1.04/0.87  % (12041)Time elapsed: 0.022 s
% 1.04/0.87  % (12041)Instructions burned: 33 (million)
% 1.04/0.87  % (12041)------------------------------
% 1.04/0.87  % (12041)------------------------------
% 1.06/0.88  % (12046)dis+1011_1:1_sil=16000:nwc=7.0:s2agt=64:s2a=on:i=1919:ss=axioms:sgt=8:lsd=50:sd=7_0 on Vampire---4 for (2994ds/1919Mi)
% 1.06/0.89  % (12040)Instruction limit reached!
% 1.06/0.89  % (12040)------------------------------
% 1.06/0.89  % (12040)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.06/0.89  % (12040)Termination reason: Unknown
% 1.06/0.89  % (12040)Termination phase: Saturation
% 1.06/0.89  
% 1.06/0.89  % (12040)Memory used [KB]: 2233
% 1.06/0.89  % (12040)Time elapsed: 0.038 s
% 1.06/0.89  % (12040)Instructions burned: 62 (million)
% 1.06/0.89  % (12040)------------------------------
% 1.06/0.89  % (12040)------------------------------
% 1.06/0.89  % (12046)First to succeed.
% 1.06/0.89  % (12048)ott-32_5:1_sil=4000:sp=occurrence:urr=full:rp=on:nwc=5.0:newcnf=on:st=5.0:s2pl=on:i=55:sd=2:ins=2:ss=included:rawr=on:anc=none:sos=on:s2agt=8:spb=intro:ep=RS:avsq=on:avsqr=27,155:lma=on_0 on Vampire---4 for (2994ds/55Mi)
% 1.06/0.89  % (12046)Refutation found. Thanks to Tanya!
% 1.06/0.89  % SZS status Theorem for Vampire---4
% 1.06/0.89  % SZS output start Proof for Vampire---4
% See solution above
% 1.06/0.90  % (12046)------------------------------
% 1.06/0.90  % (12046)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.06/0.90  % (12046)Termination reason: Refutation
% 1.06/0.90  
% 1.06/0.90  % (12046)Memory used [KB]: 1200
% 1.06/0.90  % (12046)Time elapsed: 0.017 s
% 1.06/0.90  % (12046)Instructions burned: 24 (million)
% 1.06/0.90  % (12046)------------------------------
% 1.06/0.90  % (12046)------------------------------
% 1.06/0.90  % (11994)Success in time 0.533 s
% 1.06/0.90  % Vampire---4.8 exiting
%------------------------------------------------------------------------------