TSTP Solution File: ANA079^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% 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 : n022.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 : Mon May 20 18:40:24 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   80 (   9 unt;  15 typ;   0 def)
%            Number of atoms       :  587 ( 170 equ;   0 cnn)
%            Maximal formula atoms :   10 (   9 avg)
%            Number of connectives :  776 (  97   ~;  83   |;  51   &; 511   @)
%                                         (   4 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  16 usr;   9 con; 0-3 aty)
%            Number of variables   :  156 (   0   ^ 123   !;  29   ?; 156   :)
%                                         (   4  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(type_def_5,type,
    'type/realax/real': $tType ).

thf(func_def_0,type,
    'type/realax/real': $tType ).

thf(func_def_1,type,
    'const/sets/sup': ( 'type/realax/real' > $o ) > 'type/realax/real' ).

thf(func_def_2,type,
    'const/sets/IN': 
      !>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).

thf(func_def_3,type,
    'const/sets/EMPTY': 
      !>[X0: $tType] : ( X0 > $o ) ).

thf(func_def_4,type,
    'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).

thf(func_def_8,type,
    sK0: 'type/realax/real' > $o ).

thf(func_def_9,type,
    sK1: 'type/realax/real' ).

thf(func_def_10,type,
    sK2: 'type/realax/real' ).

thf(func_def_11,type,
    sK3: 'type/realax/real' ).

thf(func_def_12,type,
    sK4: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).

thf(func_def_13,type,
    sK5: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).

thf(func_def_14,type,
    sK6: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_16,type,
    ph8: 
      !>[X0: $tType] : X0 ).

thf(func_def_17,type,
    sK9: 'type/realax/real' ).

thf(f188,plain,
    $false,
    inference(avatar_sat_refutation,[],[f77,f109,f141,f181]) ).

thf(f181,plain,
    ~ spl7_5,
    inference(avatar_contradiction_clause,[],[f180]) ).

thf(f180,plain,
    ( $false
    | ~ spl7_5 ),
    inference(subsumption_resolution,[],[f173,f32]) ).

thf(f32,plain,
    ( ( 'const/realax/real_le' @ sK1 @ sK3 )
    = $true ),
    inference(cnf_transformation,[],[f22]) ).

thf(f22,plain,
    ( ! [X4: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X4 @ sK2 )
          = $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
         != $true ) )
    & ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
      = $true )
    & ( ( 'const/realax/real_le' @ sK1 @ sK3 )
      = $true )
    & ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
     != $true ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f21]) ).

thf(f21,plain,
    ( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ! [X4: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ X4 @ X2 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             != $true ) )
        & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
          = $true )
        & ( ( 'const/realax/real_le' @ X1 @ X3 )
          = $true )
        & ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
         != $true ) )
   => ( ! [X4: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X4 @ sK2 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
           != $true ) )
      & ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
        = $true )
      & ( ( 'const/realax/real_le' @ sK1 @ sK3 )
        = $true )
      & ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
       != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f20,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
      ( ! [X4: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X4 @ X2 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
           != $true ) )
      & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
        = $true )
      & ( ( 'const/realax/real_le' @ X1 @ X3 )
        = $true )
      & ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
       != $true ) ),
    inference(flattening,[],[f19]) ).

thf(f19,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
       != $true )
      & ( ( 'const/realax/real_le' @ X1 @ X3 )
        = $true )
      & ! [X4: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X4 @ X2 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
           != $true ) )
      & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
        = $true ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,plain,
    ~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ( ( ( 'const/realax/real_le' @ X1 @ X3 )
            = $true )
          & ! [X4: 'type/realax/real'] :
              ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
                = $true )
             => ( ( 'const/realax/real_le' @ X4 @ X2 )
                = $true ) )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
            = $true ) )
       => ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
          = $true ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,plain,
    ~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ X3 )
          & ! [X4: 'type/realax/real'] :
              ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             => ( 'const/realax/real_le' @ X4 @ X2 ) )
          & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
       => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
    inference(rectify,[],[f5]) ).

thf(f5,negated_conjecture,
    ~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ X3 )
          & ! [X4: 'type/realax/real'] :
              ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             => ( 'const/realax/real_le' @ X4 @ X2 ) )
          & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
       => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
    inference(negated_conjecture,[],[f4]) ).

thf(f4,conjecture,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ X3 )
        & ! [X4: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
           => ( 'const/realax/real_le' @ X4 @ X2 ) )
        & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
     => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_') ).

thf(f173,plain,
    ( ( ( 'const/realax/real_le' @ sK1 @ sK3 )
     != $true )
    | ~ spl7_5 ),
    inference(trivial_inequality_removal,[],[f168]) ).

thf(f168,plain,
    ( ( ( 'const/realax/real_le' @ sK1 @ sK3 )
     != $true )
    | ( $true != $true )
    | ~ spl7_5 ),
    inference(superposition,[],[f147,f33]) ).

thf(f33,plain,
    ( ( 'const/sets/IN' @ 'type/realax/real' @ sK3 @ sK0 )
    = $true ),
    inference(cnf_transformation,[],[f22]) ).

thf(f147,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
         != $true )
        | ( ( 'const/realax/real_le' @ sK1 @ X0 )
         != $true ) )
    | ~ spl7_5 ),
    inference(trivial_inequality_removal,[],[f142]) ).

thf(f142,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK1 @ X0 )
         != $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
         != $true )
        | ( $true != $true ) )
    | ~ spl7_5 ),
    inference(superposition,[],[f46,f76]) ).

thf(f76,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
          = $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
         != $true ) )
    | ~ spl7_5 ),
    inference(avatar_component_clause,[],[f75]) ).

thf(f75,plain,
    ( spl7_5
  <=> ! [X1: 'type/realax/real'] :
        ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
         != $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).

thf(f46,plain,
    ! [X0: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
       != $true )
      | ( ( 'const/realax/real_le' @ sK1 @ X0 )
       != $true ) ),
    inference(trivial_inequality_removal,[],[f45]) ).

thf(f45,plain,
    ! [X0: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
       != $true )
      | ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK1 @ X0 )
       != $true ) ),
    inference(superposition,[],[f31,f43]) ).

thf(f43,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ X2 )
        = $true )
      | ( ( 'const/realax/real_le' @ X0 @ X1 )
       != $true )
      | ( ( 'const/realax/real_le' @ X1 @ X2 )
       != $true ) ),
    inference(cnf_transformation,[],[f18]) ).

thf(f18,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ X1 )
       != $true )
      | ( ( 'const/realax/real_le' @ X1 @ X2 )
       != $true )
      | ( ( 'const/realax/real_le' @ X0 @ X2 )
        = $true ) ),
    inference(flattening,[],[f17]) ).

thf(f17,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ X2 )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ X2 )
       != $true )
      | ( ( 'const/realax/real_le' @ X0 @ X1 )
       != $true ) ),
    inference(ennf_transformation,[],[f8]) ).

thf(f8,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( ( 'const/realax/real_le' @ X1 @ X2 )
          = $true )
        & ( ( 'const/realax/real_le' @ X0 @ X1 )
          = $true ) )
     => ( ( 'const/realax/real_le' @ X0 @ X2 )
        = $true ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ X1 )
        & ( 'const/realax/real_le' @ X1 @ X2 ) )
     => ( 'const/realax/real_le' @ X0 @ X2 ) ),
    inference(rectify,[],[f1]) ).

thf(f1,axiom,
    ! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ X1 )
        & ( 'const/realax/real_le' @ X1 @ X2 ) )
     => ( 'const/realax/real_le' @ X0 @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).

thf(f31,plain,
    ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
   != $true ),
    inference(cnf_transformation,[],[f22]) ).

thf(f141,plain,
    ( spl7_5
    | ~ spl7_1
    | spl7_2 ),
    inference(avatar_split_clause,[],[f140,f63,f60,f75]) ).

thf(f60,plain,
    ( spl7_1
  <=> ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
        = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).

thf(f63,plain,
    ( spl7_2
  <=> ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).

thf(f140,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
         != $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
          = $true ) )
    | ~ spl7_1
    | spl7_2 ),
    inference(subsumption_resolution,[],[f136,f64]) ).

thf(f64,plain,
    ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) )
    | spl7_2 ),
    inference(avatar_component_clause,[],[f63]) ).

thf(f136,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
          = $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
         != $true )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) )
    | ~ spl7_1 ),
    inference(trivial_inequality_removal,[],[f134]) ).

thf(f134,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/sup' @ sK0 ) )
          = $true )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
         != $true )
        | ( $true != $true ) )
    | ~ spl7_1 ),
    inference(superposition,[],[f39,f61]) ).

thf(f61,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
        = $true )
    | ~ spl7_1 ),
    inference(avatar_component_clause,[],[f60]) ).

thf(f39,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
       != $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
       != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f26,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ! [X1: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
             != $true )
            | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
              = $true ) )
        & ! [X2: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
              = $true )
            | ( ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
               != $true )
              & ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
                = $true ) ) ) )
      | ! [X4: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
            = $true )
          & ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
           != $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f23,f25,f24]) ).

thf(f24,plain,
    ! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
      ( ? [X3: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X3 @ X2 )
           != $true )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
            = $true ) )
     => ( ( ( 'const/realax/real_le' @ ( sK4 @ X2 @ X0 ) @ X2 )
         != $true )
        & ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK4 @ X2 @ X0 ) @ X0 )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f25,plain,
    ! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ? [X5: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
            = $true )
          & ( ( 'const/realax/real_le' @ X5 @ X4 )
           != $true ) )
     => ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
          = $true )
        & ( ( 'const/realax/real_le' @ ( sK5 @ X4 @ X0 ) @ X4 )
         != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f23,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ! [X1: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
             != $true )
            | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
              = $true ) )
        & ! [X2: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X2 )
              = $true )
            | ? [X3: 'type/realax/real'] :
                ( ( ( 'const/realax/real_le' @ X3 @ X2 )
                 != $true )
                & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
                  = $true ) ) ) )
      | ! [X4: 'type/realax/real'] :
        ? [X5: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
            = $true )
          & ( ( 'const/realax/real_le' @ X5 @ X4 )
           != $true ) ) ),
    inference(rectify,[],[f16]) ).

thf(f16,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             != $true )
            | ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
              = $true ) )
        & ! [X4: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
              = $true )
            | ? [X5: 'type/realax/real'] :
                ( ( ( 'const/realax/real_le' @ X5 @ X4 )
                 != $true )
                & ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true ) ) ) )
      | ! [X1: 'type/realax/real'] :
        ? [X2: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
            = $true )
          & ( ( 'const/realax/real_le' @ X2 @ X1 )
           != $true ) ) ),
    inference(flattening,[],[f15]) ).

thf(f15,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             != $true )
            | ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
              = $true ) )
        & ! [X4: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
              = $true )
            | ? [X5: 'type/realax/real'] :
                ( ( ( 'const/realax/real_le' @ X5 @ X4 )
                 != $true )
                & ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true ) ) ) )
      | ! [X1: 'type/realax/real'] :
        ? [X2: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
            = $true )
          & ( ( 'const/realax/real_le' @ X2 @ X1 )
           != $true ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(ennf_transformation,[],[f10]) ).

thf(f10,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ? [X1: 'type/realax/real'] :
          ! [X2: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
              = $true )
           => ( ( 'const/realax/real_le' @ X2 @ X1 )
              = $true ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X4: 'type/realax/real'] :
            ( ! [X5: 'type/realax/real'] :
                ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true )
               => ( ( 'const/realax/real_le' @ X5 @ X4 )
                  = $true ) )
           => ( ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 )
              = $true ) )
        & ! [X3: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
              = $true )
           => ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) )
              = $true ) ) ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f9,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ? [X1: 'type/realax/real'] :
          ! [X2: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
           => ( 'const/realax/real_le' @ X2 @ X1 ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X3: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
           => ( 'const/realax/real_le' @ X3 @ ( 'const/sets/sup' @ X0 ) ) )
        & ! [X4: 'type/realax/real'] :
            ( ! [X5: 'type/realax/real'] :
                ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
               => ( 'const/realax/real_le' @ X5 @ X4 ) )
           => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X4 ) ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,axiom,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ? [X1: 'type/realax/real'] :
          ! [X2: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
           => ( 'const/realax/real_le' @ X2 @ X1 ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X1: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
           => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
        & ! [X1: 'type/realax/real'] :
            ( ! [X2: 'type/realax/real'] :
                ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
               => ( 'const/realax/real_le' @ X2 @ X1 ) )
           => ( 'const/realax/real_le' @ ( 'const/sets/sup' @ X0 ) @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_') ).

thf(f109,plain,
    ~ spl7_2,
    inference(avatar_contradiction_clause,[],[f108]) ).

thf(f108,plain,
    ( $false
    | ~ spl7_2 ),
    inference(trivial_inequality_removal,[],[f105]) ).

thf(f105,plain,
    ( ( $true != $true )
    | ~ spl7_2 ),
    inference(superposition,[],[f91,f33]) ).

thf(f91,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 )
       != $true )
    | ~ spl7_2 ),
    inference(superposition,[],[f44,f65]) ).

thf(f65,plain,
    ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
    | ~ spl7_2 ),
    inference(avatar_component_clause,[],[f63]) ).

thf(f44,plain,
    ! [X0: $tType,X3: X0] :
      ( ( 'const/sets/IN' @ X0 @ X3 @ 'const/sets/EMPTY' @ X0 )
     != $true ),
    inference(equality_resolution,[],[f41]) ).

thf(f41,plain,
    ! [X0: $tType,X3: X0,X1: X0 > $o] :
      ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
      | ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
       != $true ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
          = $true )
        | ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
      & ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
        | ! [X3: X0] :
            ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
           != $true ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f28,f29]) ).

thf(f29,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ? [X2: X0] :
          ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
          = $true )
     => ( ( 'const/sets/IN' @ X0 @ ( sK6 @ X0 @ X1 ) @ X1 )
        = $true ) ),
    introduced(choice_axiom,[]) ).

thf(f28,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ? [X2: X0] :
            ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
            = $true )
        | ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
      & ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
        | ! [X3: X0] :
            ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
           != $true ) ) ),
    inference(rectify,[],[f27]) ).

thf(f27,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ? [X2: X0] :
            ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
            = $true )
        | ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) )
      & ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
        | ! [X2: X0] :
            ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
           != $true ) ) ),
    inference(nnf_transformation,[],[f14]) ).

thf(f14,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ? [X2: X0] :
          ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
          = $true )
    <=> ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
    inference(fool_elimination,[],[f13]) ).

thf(f13,plain,
    ! [X0: $tType,X1: X0 > $o] :
    ? [X2: X0] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
    inference(rectify,[],[f2]) ).

thf(f2,axiom,
    ! [X0: $tType,X1: X0 > $o] :
    ? [X2: X0] :
      ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
      = ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/MEMBER_NOT_EMPTY_') ).

thf(f77,plain,
    ( spl7_1
    | spl7_5
    | spl7_2 ),
    inference(avatar_split_clause,[],[f56,f63,f75,f60]) ).

thf(f56,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
       != $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
      | ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f49]) ).

thf(f49,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true != $true )
      | ( ( 'const/realax/real_le' @ ( sK5 @ X0 @ sK0 ) @ sK2 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ sK0 ) )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
       != $true ) ),
    inference(superposition,[],[f34,f40]) ).

thf(f40,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK5 @ X4 @ X0 ) @ X0 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
       != $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
        = $true ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f34,plain,
    ! [X4: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK0 )
       != $true )
      | ( ( 'const/realax/real_le' @ X4 @ sK2 )
        = $true ) ),
    inference(cnf_transformation,[],[f22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ANA079^1 : TPTP v8.2.0. Released v7.0.0.
% 0.13/0.13  % 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
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon May 20 07:42:37 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  This is a TH1_THM_EQU_NAR problem
% 0.14/0.34  Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36  % (4314)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.36  % (4312)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.36  % (4317)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.36  % (4311)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.36  % (4314)Instruction limit reached!
% 0.14/0.36  % (4314)------------------------------
% 0.14/0.36  % (4314)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36  % (4314)Termination reason: Unknown
% 0.14/0.36  % (4314)Termination phase: Property scanning
% 0.14/0.36  
% 0.14/0.36  % (4314)Memory used [KB]: 895
% 0.14/0.36  % (4314)Time elapsed: 0.003 s
% 0.14/0.36  % (4314)Instructions burned: 3 (million)
% 0.14/0.36  % (4314)------------------------------
% 0.14/0.36  % (4314)------------------------------
% 0.14/0.36  % (4317)Instruction limit reached!
% 0.14/0.36  % (4317)------------------------------
% 0.14/0.36  % (4317)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36  % (4317)Termination reason: Unknown
% 0.14/0.36  % (4317)Termination phase: Saturation
% 0.14/0.36  
% 0.14/0.36  % (4317)Memory used [KB]: 1023
% 0.14/0.36  % (4317)Time elapsed: 0.003 s
% 0.14/0.36  % (4317)Instructions burned: 3 (million)
% 0.14/0.36  % (4317)------------------------------
% 0.14/0.36  % (4317)------------------------------
% 0.14/0.36  % (4315)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.37  % (4310)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37  % (4311)Instruction limit reached!
% 0.14/0.37  % (4311)------------------------------
% 0.14/0.37  % (4311)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (4311)Termination reason: Unknown
% 0.14/0.37  % (4311)Termination phase: Saturation
% 0.14/0.37  
% 0.14/0.37  % (4311)Memory used [KB]: 5500
% 0.14/0.37  % (4311)Time elapsed: 0.005 s
% 0.14/0.37  % (4311)Instructions burned: 5 (million)
% 0.14/0.37  % (4311)------------------------------
% 0.14/0.37  % (4311)------------------------------
% 0.14/0.37  % (4313)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37  % (4313)Instruction limit reached!
% 0.14/0.37  % (4313)------------------------------
% 0.14/0.37  % (4313)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37  % (4313)Termination reason: Unknown
% 0.14/0.37  % (4313)Termination phase: Property scanning
% 0.14/0.37  
% 0.14/0.37  % (4313)Memory used [KB]: 895
% 0.14/0.37  % (4313)Time elapsed: 0.003 s
% 0.14/0.37  % (4313)Instructions burned: 2 (million)
% 0.14/0.37  % (4313)------------------------------
% 0.14/0.37  % (4313)------------------------------
% 0.14/0.37  % (4316)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37  % (4315)First to succeed.
% 0.14/0.38  % (4318)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.38  % (4310)Also succeeded, but the first one will report.
% 0.14/0.38  % (4315)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (4315)------------------------------
% 0.14/0.38  % (4315)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38  % (4315)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (4315)Memory used [KB]: 5628
% 0.14/0.38  % (4315)Time elapsed: 0.014 s
% 0.14/0.38  % (4315)Instructions burned: 19 (million)
% 0.14/0.38  % (4315)------------------------------
% 0.14/0.38  % (4315)------------------------------
% 0.14/0.38  % (4309)Success in time 0.028 s
% 0.14/0.38  % Vampire---4.8 exiting
%------------------------------------------------------------------------------