TSTP Solution File: NUM401+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM401+1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 08:11:37 EDT 2024

% Result   : Theorem 0.80s 0.80s
% Output   : Refutation 0.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  117 (  11 unt;   0 def)
%            Number of atoms       :  435 (  57 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  502 ( 184   ~; 208   |;  75   &)
%                                         (  20 <=>;  14  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   16 (  14 usr;   9 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-3 aty)
%            Number of variables   :  134 ( 114   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1062,plain,
    $false,
    inference(avatar_sat_refutation,[],[f276,f279,f534,f543,f548,f677,f688,f701,f719,f728,f764,f1061]) ).

fof(f1061,plain,
    ( spl19_1
    | ~ spl19_18 ),
    inference(avatar_contradiction_clause,[],[f1051]) ).

fof(f1051,plain,
    ( $false
    | spl19_1
    | ~ spl19_18 ),
    inference(resolution,[],[f779,f272]) ).

fof(f272,plain,
    ( ~ in(sK0,set_union2(sK1,singleton(sK1)))
    | spl19_1 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl19_1
  <=> in(sK0,set_union2(sK1,singleton(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).

fof(f779,plain,
    ( ! [X0] : in(sK0,set_union2(sK1,X0))
    | ~ spl19_18 ),
    inference(resolution,[],[f638,f263]) ).

fof(f263,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,X0)
      | in(X4,set_union2(X0,X1)) ),
    inference(equality_resolution,[],[f162]) ).

fof(f162,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | ~ in(X4,X0)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ( ( ( ~ in(sK2(X0,X1,X2),X1)
              & ~ in(sK2(X0,X1,X2),X0) )
            | ~ in(sK2(X0,X1,X2),X2) )
          & ( in(sK2(X0,X1,X2),X1)
            | in(sK2(X0,X1,X2),X0)
            | in(sK2(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f107,f108]) ).

fof(f108,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X1)
              & ~ in(X3,X0) )
            | ~ in(X3,X2) )
          & ( in(X3,X1)
            | in(X3,X0)
            | in(X3,X2) ) )
     => ( ( ( ~ in(sK2(X0,X1,X2),X1)
            & ~ in(sK2(X0,X1,X2),X0) )
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( in(sK2(X0,X1,X2),X1)
          | in(sK2(X0,X1,X2),X0)
          | in(sK2(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( ~ in(X4,X1)
                & ~ in(X4,X0) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | ~ in(X4,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(rectify,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X0,X1) = X2
        | ? [X3] :
            ( ( ( ~ in(X3,X1)
                & ~ in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X1)
              | in(X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( ~ in(X3,X1)
                & ~ in(X3,X0) ) )
            & ( in(X3,X1)
              | in(X3,X0)
              | ~ in(X3,X2) ) )
        | set_union2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',d2_xboole_0) ).

fof(f638,plain,
    ( in(sK0,sK1)
    | ~ spl19_18 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f637,plain,
    ( spl19_18
  <=> in(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).

fof(f764,plain,
    ( spl19_2
    | ~ spl19_10 ),
    inference(avatar_contradiction_clause,[],[f763]) ).

fof(f763,plain,
    ( $false
    | spl19_2
    | ~ spl19_10 ),
    inference(subsumption_resolution,[],[f742,f268]) ).

fof(f268,plain,
    ! [X1] : subset(X1,X1),
    inference(equality_resolution,[],[f221]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | X0 != X1 ),
    inference(cnf_transformation,[],[f133]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f132]) ).

fof(f132,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',d10_xboole_0) ).

fof(f742,plain,
    ( ~ subset(sK1,sK1)
    | spl19_2
    | ~ spl19_10 ),
    inference(backward_demodulation,[],[f694,f533]) ).

fof(f533,plain,
    ( sK0 = sK1
    | ~ spl19_10 ),
    inference(avatar_component_clause,[],[f532]) ).

fof(f532,plain,
    ( spl19_10
  <=> sK0 = sK1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).

fof(f694,plain,
    ( ~ subset(sK0,sK1)
    | spl19_2 ),
    inference(subsumption_resolution,[],[f693,f150]) ).

fof(f150,plain,
    ordinal(sK0),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( ( ~ ordinal_subset(sK0,sK1)
      | ~ in(sK0,succ(sK1)) )
    & ( ordinal_subset(sK0,sK1)
      | in(sK0,succ(sK1)) )
    & ordinal(sK1)
    & ordinal(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f101,f103,f102]) ).

fof(f102,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ ordinal_subset(X0,X1)
              | ~ in(X0,succ(X1)) )
            & ( ordinal_subset(X0,X1)
              | in(X0,succ(X1)) )
            & ordinal(X1) )
        & ordinal(X0) )
   => ( ? [X1] :
          ( ( ~ ordinal_subset(sK0,X1)
            | ~ in(sK0,succ(X1)) )
          & ( ordinal_subset(sK0,X1)
            | in(sK0,succ(X1)) )
          & ordinal(X1) )
      & ordinal(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ( ? [X1] :
        ( ( ~ ordinal_subset(sK0,X1)
          | ~ in(sK0,succ(X1)) )
        & ( ordinal_subset(sK0,X1)
          | in(sK0,succ(X1)) )
        & ordinal(X1) )
   => ( ( ~ ordinal_subset(sK0,sK1)
        | ~ in(sK0,succ(sK1)) )
      & ( ordinal_subset(sK0,sK1)
        | in(sK0,succ(sK1)) )
      & ordinal(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f101,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(X0,X1)
            | ~ in(X0,succ(X1)) )
          & ( ordinal_subset(X0,X1)
            | in(X0,succ(X1)) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(flattening,[],[f100]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ ordinal_subset(X0,X1)
            | ~ in(X0,succ(X1)) )
          & ( ordinal_subset(X0,X1)
            | in(X0,succ(X1)) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( in(X0,succ(X1))
          <~> ordinal_subset(X0,X1) )
          & ordinal(X1) )
      & ordinal(X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X0] :
        ( ordinal(X0)
       => ! [X1] :
            ( ordinal(X1)
           => ( in(X0,succ(X1))
            <=> ordinal_subset(X0,X1) ) ) ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ( in(X0,succ(X1))
          <=> ordinal_subset(X0,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',t34_ordinal1) ).

fof(f693,plain,
    ( ~ subset(sK0,sK1)
    | ~ ordinal(sK0)
    | spl19_2 ),
    inference(subsumption_resolution,[],[f690,f151]) ).

fof(f151,plain,
    ordinal(sK1),
    inference(cnf_transformation,[],[f104]) ).

fof(f690,plain,
    ( ~ subset(sK0,sK1)
    | ~ ordinal(sK1)
    | ~ ordinal(sK0)
    | spl19_2 ),
    inference(resolution,[],[f275,f184]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( ordinal_subset(X0,X1)
      | ~ subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f118,plain,
    ! [X0,X1] :
      ( ( ( ordinal_subset(X0,X1)
          | ~ subset(X0,X1) )
        & ( subset(X0,X1)
          | ~ ordinal_subset(X0,X1) ) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(nnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) )
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1] :
      ( ( ordinal(X1)
        & ordinal(X0) )
     => ( ordinal_subset(X0,X1)
      <=> subset(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',redefinition_r1_ordinal1) ).

fof(f275,plain,
    ( ~ ordinal_subset(sK0,sK1)
    | spl19_2 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f274,plain,
    ( spl19_2
  <=> ordinal_subset(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).

fof(f728,plain,
    spl19_25,
    inference(avatar_contradiction_clause,[],[f727]) ).

fof(f727,plain,
    ( $false
    | spl19_25 ),
    inference(subsumption_resolution,[],[f725,f151]) ).

fof(f725,plain,
    ( ~ ordinal(sK1)
    | spl19_25 ),
    inference(resolution,[],[f699,f209]) ).

fof(f209,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,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/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',cc1_ordinal1) ).

fof(f699,plain,
    ( ~ epsilon_transitive(sK1)
    | spl19_25 ),
    inference(avatar_component_clause,[],[f698]) ).

fof(f698,plain,
    ( spl19_25
  <=> epsilon_transitive(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).

fof(f719,plain,
    ( spl19_10
    | ~ spl19_1
    | spl19_18 ),
    inference(avatar_split_clause,[],[f714,f637,f271,f532]) ).

fof(f714,plain,
    ( sK0 = sK1
    | ~ spl19_1
    | spl19_18 ),
    inference(resolution,[],[f713,f267]) ).

fof(f267,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f170]) ).

fof(f170,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f117]) ).

fof(f117,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | X0 != X3 )
            & ( X0 = X3
              | ~ in(X3,X1) ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f115,f116]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( X0 != X2
            | ~ in(X2,X1) )
          & ( X0 = X2
            | in(X2,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(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,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',d1_tarski) ).

fof(f713,plain,
    ( in(sK0,singleton(sK1))
    | ~ spl19_1
    | spl19_18 ),
    inference(subsumption_resolution,[],[f708,f700]) ).

fof(f700,plain,
    ( ~ in(sK0,sK1)
    | spl19_18 ),
    inference(avatar_component_clause,[],[f637]) ).

fof(f708,plain,
    ( in(sK0,sK1)
    | in(sK0,singleton(sK1))
    | ~ spl19_1 ),
    inference(resolution,[],[f277,f264]) ).

fof(f264,plain,
    ! [X0,X1,X4] :
      ( ~ in(X4,set_union2(X0,X1))
      | in(X4,X0)
      | in(X4,X1) ),
    inference(equality_resolution,[],[f161]) ).

fof(f161,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | in(X4,X0)
      | ~ in(X4,X2)
      | set_union2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f109]) ).

fof(f277,plain,
    ( in(sK0,set_union2(sK1,singleton(sK1)))
    | ~ spl19_1 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f701,plain,
    ( ~ spl19_25
    | ~ spl19_18
    | spl19_2 ),
    inference(avatar_split_clause,[],[f695,f274,f637,f698]) ).

fof(f695,plain,
    ( ~ in(sK0,sK1)
    | ~ epsilon_transitive(sK1)
    | spl19_2 ),
    inference(resolution,[],[f694,f167]) ).

fof(f167,plain,
    ! [X2,X0] :
      ( subset(X2,X0)
      | ~ in(X2,X0)
      | ~ epsilon_transitive(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ( ~ subset(sK3(X0),X0)
          & in(sK3(X0),X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f111,f112]) ).

fof(f112,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ subset(X1,X0)
          & in(X1,X0) )
     => ( ~ subset(sK3(X0),X0)
        & in(sK3(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ( epsilon_transitive(X0)
        | ? [X1] :
            ( ~ subset(X1,X0)
            & in(X1,X0) ) )
      & ( ! [X2] :
            ( subset(X2,X0)
            | ~ in(X2,X0) )
        | ~ epsilon_transitive(X0) ) ),
    inference(rectify,[],[f110]) ).

fof(f110,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,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( subset(X1,X0)
          | ~ in(X1,X0) ) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( epsilon_transitive(X0)
    <=> ! [X1] :
          ( in(X1,X0)
         => subset(X1,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',d2_ordinal1) ).

fof(f688,plain,
    ( spl19_12
    | spl19_10
    | spl19_18 ),
    inference(avatar_split_clause,[],[f612,f637,f532,f541]) ).

fof(f541,plain,
    ( spl19_12
  <=> in(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).

fof(f612,plain,
    ( in(sK0,sK1)
    | sK0 = sK1
    | in(sK1,sK0) ),
    inference(resolution,[],[f582,f151]) ).

fof(f582,plain,
    ! [X0] :
      ( ~ ordinal(X0)
      | in(sK0,X0)
      | sK0 = X0
      | in(X0,sK0) ),
    inference(resolution,[],[f158,f150]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ~ ordinal(X0)
      | X0 = X1
      | in(X0,X1)
      | ~ ordinal(X1)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ! [X1] :
          ( in(X1,X0)
          | X0 = X1
          | in(X0,X1)
          | ~ ordinal(X1) )
      | ~ ordinal(X0) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,axiom,
    ! [X0] :
      ( ordinal(X0)
     => ! [X1] :
          ( ordinal(X1)
         => ~ ( ~ in(X1,X0)
              & X0 != X1
              & ~ in(X0,X1) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',t24_ordinal1) ).

fof(f677,plain,
    ( spl19_1
    | ~ spl19_10 ),
    inference(avatar_contradiction_clause,[],[f676]) ).

fof(f676,plain,
    ( $false
    | spl19_1
    | ~ spl19_10 ),
    inference(subsumption_resolution,[],[f661,f255]) ).

fof(f255,plain,
    ! [X0] : in(X0,set_union2(X0,singleton(X0))),
    inference(definition_unfolding,[],[f160,f181]) ).

fof(f181,plain,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',d1_ordinal1) ).

fof(f160,plain,
    ! [X0] : in(X0,succ(X0)),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0] : in(X0,succ(X0)),
    file('/export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577',t10_ordinal1) ).

fof(f661,plain,
    ( ~ in(sK1,set_union2(sK1,singleton(sK1)))
    | spl19_1
    | ~ spl19_10 ),
    inference(backward_demodulation,[],[f272,f533]) ).

fof(f548,plain,
    spl19_11,
    inference(avatar_contradiction_clause,[],[f547]) ).

fof(f547,plain,
    ( $false
    | spl19_11 ),
    inference(subsumption_resolution,[],[f545,f150]) ).

fof(f545,plain,
    ( ~ ordinal(sK0)
    | spl19_11 ),
    inference(resolution,[],[f539,f209]) ).

fof(f539,plain,
    ( ~ epsilon_transitive(sK0)
    | spl19_11 ),
    inference(avatar_component_clause,[],[f538]) ).

fof(f538,plain,
    ( spl19_11
  <=> epsilon_transitive(sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).

fof(f543,plain,
    ( ~ spl19_11
    | ~ spl19_12
    | spl19_9 ),
    inference(avatar_split_clause,[],[f535,f529,f541,f538]) ).

fof(f529,plain,
    ( spl19_9
  <=> subset(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).

fof(f535,plain,
    ( ~ in(sK1,sK0)
    | ~ epsilon_transitive(sK0)
    | spl19_9 ),
    inference(resolution,[],[f530,f167]) ).

fof(f530,plain,
    ( ~ subset(sK1,sK0)
    | spl19_9 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f534,plain,
    ( ~ spl19_9
    | spl19_10
    | ~ spl19_2 ),
    inference(avatar_split_clause,[],[f527,f274,f532,f529]) ).

fof(f527,plain,
    ( sK0 = sK1
    | ~ subset(sK1,sK0)
    | ~ spl19_2 ),
    inference(resolution,[],[f522,f222]) ).

fof(f222,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f133]) ).

fof(f522,plain,
    ( subset(sK0,sK1)
    | ~ spl19_2 ),
    inference(subsumption_resolution,[],[f521,f150]) ).

fof(f521,plain,
    ( subset(sK0,sK1)
    | ~ ordinal(sK0)
    | ~ spl19_2 ),
    inference(subsumption_resolution,[],[f518,f151]) ).

fof(f518,plain,
    ( subset(sK0,sK1)
    | ~ ordinal(sK1)
    | ~ ordinal(sK0)
    | ~ spl19_2 ),
    inference(resolution,[],[f183,f278]) ).

fof(f278,plain,
    ( ordinal_subset(sK0,sK1)
    | ~ spl19_2 ),
    inference(avatar_component_clause,[],[f274]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( ~ ordinal_subset(X0,X1)
      | subset(X0,X1)
      | ~ ordinal(X1)
      | ~ ordinal(X0) ),
    inference(cnf_transformation,[],[f118]) ).

fof(f279,plain,
    ( spl19_1
    | spl19_2 ),
    inference(avatar_split_clause,[],[f254,f274,f271]) ).

fof(f254,plain,
    ( ordinal_subset(sK0,sK1)
    | in(sK0,set_union2(sK1,singleton(sK1))) ),
    inference(definition_unfolding,[],[f152,f181]) ).

fof(f152,plain,
    ( ordinal_subset(sK0,sK1)
    | in(sK0,succ(sK1)) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f276,plain,
    ( ~ spl19_1
    | ~ spl19_2 ),
    inference(avatar_split_clause,[],[f253,f274,f271]) ).

fof(f253,plain,
    ( ~ ordinal_subset(sK0,sK1)
    | ~ in(sK0,set_union2(sK1,singleton(sK1))) ),
    inference(definition_unfolding,[],[f153,f181]) ).

fof(f153,plain,
    ( ~ ordinal_subset(sK0,sK1)
    | ~ in(sK0,succ(sK1)) ),
    inference(cnf_transformation,[],[f104]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem    : NUM401+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37  % Computer : n009.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Fri May  3 15:10:38 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.16/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.SUlBATD1jP/Vampire---4.8_16577
% 0.58/0.75  % (16842)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 (2996ds/83Mi)
% 0.58/0.75  % (16836)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 (2996ds/34Mi)
% 0.58/0.75  % (16838)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.75  % (16839)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.75  % (16841)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.75  % (16843)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 (2996ds/56Mi)
% 0.58/0.75  % (16840)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 (2996ds/34Mi)
% 0.58/0.75  % (16841)Refutation not found, incomplete strategy% (16841)------------------------------
% 0.58/0.75  % (16841)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (16841)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.75  
% 0.58/0.75  % (16841)Memory used [KB]: 1062
% 0.58/0.75  % (16841)Time elapsed: 0.004 s
% 0.58/0.75  % (16841)Instructions burned: 3 (million)
% 0.58/0.75  % (16843)Refutation not found, incomplete strategy% (16843)------------------------------
% 0.58/0.75  % (16843)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75  % (16843)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.75  
% 0.58/0.75  % (16843)Memory used [KB]: 1052
% 0.58/0.75  % (16843)Time elapsed: 0.003 s
% 0.58/0.75  % (16843)Instructions burned: 3 (million)
% 0.58/0.75  % (16841)------------------------------
% 0.58/0.75  % (16841)------------------------------
% 0.58/0.75  % (16843)------------------------------
% 0.58/0.75  % (16843)------------------------------
% 0.58/0.76  % (16840)Refutation not found, incomplete strategy% (16840)------------------------------
% 0.58/0.76  % (16840)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.76  % (16840)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.76  
% 0.58/0.76  % (16840)Memory used [KB]: 1138
% 0.58/0.76  % (16840)Time elapsed: 0.004 s
% 0.58/0.76  % (16840)Instructions burned: 5 (million)
% 0.58/0.76  % (16840)------------------------------
% 0.58/0.76  % (16840)------------------------------
% 0.58/0.76  % (16837)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 (2996ds/51Mi)
% 0.58/0.76  % (16844)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 (2996ds/55Mi)
% 0.58/0.76  % (16846)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 (2996ds/208Mi)
% 0.58/0.76  % (16845)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 (2996ds/50Mi)
% 0.58/0.77  % (16839)Instruction limit reached!
% 0.58/0.77  % (16839)------------------------------
% 0.58/0.77  % (16839)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (16839)Termination reason: Unknown
% 0.58/0.77  % (16839)Termination phase: Saturation
% 0.58/0.77  
% 0.58/0.77  % (16839)Memory used [KB]: 1387
% 0.58/0.77  % (16839)Time elapsed: 0.017 s
% 0.58/0.77  % (16839)Instructions burned: 35 (million)
% 0.58/0.77  % (16839)------------------------------
% 0.58/0.77  % (16839)------------------------------
% 0.58/0.77  % (16836)Instruction limit reached!
% 0.58/0.77  % (16836)------------------------------
% 0.58/0.77  % (16836)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (16836)Termination reason: Unknown
% 0.58/0.77  % (16836)Termination phase: Saturation
% 0.58/0.77  
% 0.58/0.77  % (16836)Memory used [KB]: 1283
% 0.58/0.77  % (16836)Time elapsed: 0.020 s
% 0.58/0.77  % (16836)Instructions burned: 34 (million)
% 0.58/0.77  % (16836)------------------------------
% 0.58/0.77  % (16836)------------------------------
% 0.58/0.77  % (16847)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 (2996ds/52Mi)
% 0.58/0.77  % (16848)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 (2996ds/518Mi)
% 0.58/0.78  % (16848)Refutation not found, incomplete strategy% (16848)------------------------------
% 0.58/0.78  % (16848)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (16848)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.78  % (16842)Instruction limit reached!
% 0.58/0.78  % (16842)------------------------------
% 0.58/0.78  % (16842)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (16842)Termination reason: Unknown
% 0.58/0.78  % (16842)Termination phase: Saturation
% 0.58/0.78  
% 0.58/0.78  % (16842)Memory used [KB]: 2359
% 0.58/0.78  % (16842)Time elapsed: 0.031 s
% 0.58/0.78  % (16842)Instructions burned: 83 (million)
% 0.58/0.78  % (16842)------------------------------
% 0.58/0.78  % (16842)------------------------------
% 0.58/0.78  
% 0.58/0.78  % (16848)Memory used [KB]: 1166
% 0.58/0.78  % (16848)Time elapsed: 0.007 s
% 0.58/0.78  % (16848)Instructions burned: 9 (million)
% 0.58/0.78  % (16848)------------------------------
% 0.58/0.78  % (16848)------------------------------
% 0.58/0.78  % (16849)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 (2996ds/42Mi)
% 0.58/0.78  % (16837)Instruction limit reached!
% 0.58/0.78  % (16837)------------------------------
% 0.58/0.78  % (16837)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (16837)Termination reason: Unknown
% 0.58/0.78  % (16837)Termination phase: Saturation
% 0.58/0.78  
% 0.58/0.78  % (16837)Memory used [KB]: 1604
% 0.58/0.78  % (16837)Time elapsed: 0.030 s
% 0.58/0.78  % (16837)Instructions burned: 52 (million)
% 0.58/0.78  % (16837)------------------------------
% 0.58/0.78  % (16837)------------------------------
% 0.58/0.79  % (16844)Instruction limit reached!
% 0.58/0.79  % (16844)------------------------------
% 0.58/0.79  % (16844)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.79  % (16844)Termination reason: Unknown
% 0.58/0.79  % (16844)Termination phase: Saturation
% 0.58/0.79  
% 0.58/0.79  % (16844)Memory used [KB]: 1833
% 0.58/0.79  % (16844)Time elapsed: 0.032 s
% 0.58/0.79  % (16844)Instructions burned: 55 (million)
% 0.58/0.79  % (16844)------------------------------
% 0.58/0.79  % (16844)------------------------------
% 0.58/0.79  % (16845)Instruction limit reached!
% 0.58/0.79  % (16845)------------------------------
% 0.58/0.79  % (16845)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.79  % (16845)Termination reason: Unknown
% 0.58/0.79  % (16845)Termination phase: Saturation
% 0.58/0.79  
% 0.58/0.79  % (16845)Memory used [KB]: 1469
% 0.58/0.79  % (16845)Time elapsed: 0.030 s
% 0.58/0.79  % (16845)Instructions burned: 50 (million)
% 0.58/0.79  % (16845)------------------------------
% 0.58/0.79  % (16845)------------------------------
% 0.58/0.79  % (16851)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)
% 0.58/0.79  % (16850)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 (2996ds/243Mi)
% 0.58/0.79  % (16852)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)
% 0.80/0.79  % (16853)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)
% 0.80/0.80  % (16847)First to succeed.
% 0.80/0.80  % (16849)Instruction limit reached!
% 0.80/0.80  % (16849)------------------------------
% 0.80/0.80  % (16849)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.80/0.80  % (16849)Termination reason: Unknown
% 0.80/0.80  % (16849)Termination phase: Saturation
% 0.80/0.80  
% 0.80/0.80  % (16849)Memory used [KB]: 1612
% 0.80/0.80  % (16847)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16832"
% 0.80/0.80  % (16849)Time elapsed: 0.016 s
% 0.80/0.80  % (16849)Instructions burned: 44 (million)
% 0.80/0.80  % (16849)------------------------------
% 0.80/0.80  % (16849)------------------------------
% 0.80/0.80  % (16847)Refutation found. Thanks to Tanya!
% 0.80/0.80  % SZS status Theorem for Vampire---4
% 0.80/0.80  % SZS output start Proof for Vampire---4
% See solution above
% 0.80/0.80  % (16847)------------------------------
% 0.80/0.80  % (16847)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.80/0.80  % (16847)Termination reason: Refutation
% 0.80/0.80  
% 0.80/0.80  % (16847)Memory used [KB]: 1377
% 0.80/0.80  % (16847)Time elapsed: 0.028 s
% 0.80/0.80  % (16847)Instructions burned: 40 (million)
% 0.80/0.80  % (16832)Success in time 0.413 s
% 0.80/0.80  % Vampire---4.8 exiting
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