TSTP Solution File: ANA086^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA086^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n006.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 18:40:25 EDT 2024

% Result   : Theorem 0.23s 0.41s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   75 (   2 unt;  12 typ;   0 def)
%            Number of atoms       :  611 ( 164 equ;   0 cnn)
%            Maximal formula atoms :   10 (   9 avg)
%            Number of connectives :  785 (  99   ~; 106   |;  33   &; 516   @)
%                                         (   5 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   34 (  34   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   18 (  15 usr;   9 con; 0-3 aty)
%            Number of variables   :  114 (   0   ^  96   !;  15   ?; 114   :)
%                                         (   3  !>;   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/inf': ( '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' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).

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

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

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

thf(func_def_13,type,
    ph5: 
      !>[X0: $tType] : X0 ).

thf(func_def_14,type,
    sK6: 'type/realax/real' ).

thf(f131,plain,
    $false,
    inference(avatar_sat_refutation,[],[f75,f80,f85,f99,f104,f115,f130]) ).

thf(f130,plain,
    ( spl4_5
    | ~ spl4_8 ),
    inference(avatar_split_clause,[],[f129,f73,f62]) ).

thf(f62,plain,
    ( spl4_5
  <=> ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

thf(f73,plain,
    ( spl4_8
  <=> ! [X1: 'type/realax/real'] :
        ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

thf(f129,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
    | ~ spl4_8 ),
    inference(trivial_inequality_removal,[],[f126]) ).

thf(f126,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true != $true )
        | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
          = $true ) )
    | ~ spl4_8 ),
    inference(superposition,[],[f26,f74]) ).

thf(f74,plain,
    ( ! [X1: 'type/realax/real'] :
        ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f73]) ).

thf(f26,plain,
    ! [X2: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
       != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ X2 )
        = $true ) ),
    inference(cnf_transformation,[],[f17]) ).

thf(f17,plain,
    ( ! [X2: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ X2 )
          = $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
         != $true ) )
    & ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
     != $true )
    & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f10,f16]) ).

thf(f16,plain,
    ( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
        ( ! [X2: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ X1 @ X2 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
             != $true ) )
        & ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
         != $true )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
   => ( ! [X2: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ sK3 @ X2 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK2 )
           != $true ) )
      & ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
       != $true )
      & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ) ),
    introduced(choice_axiom,[]) ).

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

thf(f9,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
       != $true )
      & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
      & ! [X2: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ X2 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
           != $true ) ) ),
    inference(ennf_transformation,[],[f6]) ).

thf(f6,plain,
    ~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
        ( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
          & ! [X2: 'type/realax/real'] :
              ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
                = $true )
             => ( ( 'const/realax/real_le' @ X1 @ X2 )
                = $true ) ) )
       => ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
          = $true ) ),
    inference(fool_elimination,[],[f5]) ).

thf(f5,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' @ X1 @ X2 ) )
          & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
       => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
    inference(rectify,[],[f3]) ).

thf(f3,negated_conjecture,
    ~ ! [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' @ X1 @ X2 ) )
          & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
       => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
    inference(negated_conjecture,[],[f2]) ).

thf(f2,conjecture,
    ! [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' @ X1 @ X2 ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_LE_INF_') ).

thf(f115,plain,
    ( ~ spl4_7
    | ~ spl4_10 ),
    inference(avatar_contradiction_clause,[],[f114]) ).

thf(f114,plain,
    ( $false
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(subsumption_resolution,[],[f113,f25]) ).

thf(f25,plain,
    ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
   != $true ),
    inference(cnf_transformation,[],[f17]) ).

thf(f113,plain,
    ( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
      = $true )
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(trivial_inequality_removal,[],[f112]) ).

thf(f112,plain,
    ( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
      = $true )
    | ( $true != $true )
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(duplicate_literal_removal,[],[f110]) ).

thf(f110,plain,
    ( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
      = $true )
    | ( $true != $true )
    | ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
      = $true )
    | ~ spl4_7
    | ~ spl4_10 ),
    inference(superposition,[],[f84,f71]) ).

thf(f71,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl4_7 ),
    inference(avatar_component_clause,[],[f70]) ).

thf(f70,plain,
    ( spl4_7
  <=> ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

thf(f84,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
         != $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl4_10 ),
    inference(avatar_component_clause,[],[f83]) ).

thf(f83,plain,
    ( spl4_10
  <=> ! [X1: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
         != $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

thf(f104,plain,
    ( ~ spl4_5
    | ~ spl4_9 ),
    inference(avatar_contradiction_clause,[],[f103]) ).

thf(f103,plain,
    ( $false
    | ~ spl4_5
    | ~ spl4_9 ),
    inference(trivial_inequality_removal,[],[f101]) ).

thf(f101,plain,
    ( ( $true != $true )
    | ~ spl4_5
    | ~ spl4_9 ),
    inference(superposition,[],[f79,f63]) ).

thf(f63,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
    | ~ spl4_5 ),
    inference(avatar_component_clause,[],[f62]) ).

thf(f79,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
       != $true )
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f78]) ).

thf(f78,plain,
    ( spl4_9
  <=> ! [X1: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
       != $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

thf(f99,plain,
    ( spl4_9
    | ~ spl4_7 ),
    inference(avatar_split_clause,[],[f98,f70,f78]) ).

thf(f98,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
       != $true )
    | ~ spl4_7 ),
    inference(subsumption_resolution,[],[f97,f24]) ).

thf(f24,plain,
    'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
    inference(cnf_transformation,[],[f17]) ).

thf(f97,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true ) )
    | ~ spl4_7 ),
    inference(subsumption_resolution,[],[f96,f25]) ).

thf(f96,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true )
        | ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
    | ~ spl4_7 ),
    inference(trivial_inequality_removal,[],[f95]) ).

thf(f95,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( $true != $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true )
        | ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl4_7 ),
    inference(duplicate_literal_removal,[],[f94]) ).

thf(f94,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( $true != $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl4_7 ),
    inference(superposition,[],[f21,f71]) ).

thf(f21,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
       != $true )
      | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
       != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f15,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ! [X1: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
           != $true )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
            = $true ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             != $true ) )
        & ! [X4: 'type/realax/real'] :
            ( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
                = $true )
              & ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
               != $true ) )
            | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f14,f13]) ).

thf(f13,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
      ( ? [X2: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ X2 )
           != $true )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
            = $true ) )
     => ( ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
         != $true )
        & ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
          = $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f14,plain,
    ! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ? [X5: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
            = $true )
          & ( $true
           != ( 'const/realax/real_le' @ X4 @ X5 ) ) )
     => ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
          = $true )
        & ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
         != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f12,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ! [X1: 'type/realax/real'] :
        ? [X2: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ X2 )
           != $true )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
            = $true ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
              = $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 )
                & ( $true
                 != ( 'const/realax/real_le' @ X4 @ X5 ) ) )
            | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) ) ) ),
    inference(flattening,[],[f11]) ).

thf(f11,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
              = $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 )
                & ( $true
                 != ( 'const/realax/real_le' @ X4 @ X5 ) ) )
            | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) ) )
      | ! [X1: 'type/realax/real'] :
        ? [X2: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ X2 )
           != $true )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
            = $true ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(ennf_transformation,[],[f8]) ).

thf(f8,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' @ X1 @ X2 )
              = $true ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X3: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
              = $true )
           => ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 )
              = $true ) )
        & ! [X4: 'type/realax/real'] :
            ( ! [X5: 'type/realax/real'] :
                ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true )
               => ( $true
                  = ( 'const/realax/real_le' @ X4 @ X5 ) ) )
           => ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) ) ) ),
    inference(fool_elimination,[],[f7]) ).

thf(f7,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' @ X1 @ X2 ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X3: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
           => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
        & ! [X4: 'type/realax/real'] :
            ( ! [X5: 'type/realax/real'] :
                ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
               => ( 'const/realax/real_le' @ X4 @ X5 ) )
           => ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
    inference(rectify,[],[f1]) ).

thf(f1,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' @ X1 @ X2 ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ! [X1: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
           => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) )
        & ! [X1: 'type/realax/real'] :
            ( ! [X2: 'type/realax/real'] :
                ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
               => ( 'const/realax/real_le' @ X1 @ X2 ) )
           => ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_') ).

thf(f85,plain,
    ( spl4_10
    | spl4_5 ),
    inference(avatar_split_clause,[],[f81,f62,f83]) ).

thf(f81,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
       != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true ) ),
    inference(subsumption_resolution,[],[f56,f24]) ).

thf(f56,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
       != $true ) ),
    inference(trivial_inequality_removal,[],[f52]) ).

thf(f52,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) )
       != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
    inference(superposition,[],[f26,f18]) ).

thf(f18,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
        = $true )
      | ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
       != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
        = $true ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f80,plain,
    ( spl4_9
    | spl4_7 ),
    inference(avatar_split_clause,[],[f76,f70,f78]) ).

thf(f76,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
       != $true ) ),
    inference(subsumption_resolution,[],[f57,f24]) ).

thf(f57,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
       != $true ) ),
    inference(trivial_inequality_removal,[],[f54]) ).

thf(f54,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) )
       != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( $true != $true ) ),
    inference(superposition,[],[f26,f22]) ).

thf(f22,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) )
       != $true )
      | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f15]) ).

thf(f75,plain,
    ( spl4_7
    | spl4_8 ),
    inference(avatar_split_clause,[],[f68,f73,f70]) ).

thf(f68,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
      | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true ) ),
    inference(subsumption_resolution,[],[f58,f24]) ).

thf(f58,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f55]) ).

thf(f55,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( $true != $true ) ),
    inference(superposition,[],[f26,f19]) ).

thf(f19,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
        = $true )
      | ( ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : ANA086^1 : TPTP v8.2.0. Released v7.0.0.
% 0.04/0.14  % 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
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 07:58:23 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TH1_THM_EQU_NAR problem
% 0.23/0.37  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/sandbox/benchmark/theBenchmark.p
% 0.23/0.39  % (3317)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)
% 0.23/0.40  % (3315)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.23/0.40  % (3316)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)
% 0.23/0.40  % (3318)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.23/0.40  % (3319)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)
% 0.23/0.40  % (3321)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.23/0.40  % (3320)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)
% 0.23/0.40  % (3322)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)
% 0.23/0.40  % (3318)Instruction limit reached!
% 0.23/0.40  % (3318)------------------------------
% 0.23/0.40  % (3318)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (3318)Termination reason: Unknown
% 0.23/0.40  % (3318)Termination phase: Preprocessing 3
% 0.23/0.40  
% 0.23/0.40  % (3318)Memory used [KB]: 895
% 0.23/0.40  % (3318)Time elapsed: 0.004 s
% 0.23/0.40  % (3318)Instructions burned: 2 (million)
% 0.23/0.40  % (3318)------------------------------
% 0.23/0.40  % (3318)------------------------------
% 0.23/0.40  % (3319)Instruction limit reached!
% 0.23/0.40  % (3319)------------------------------
% 0.23/0.40  % (3319)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (3319)Termination reason: Unknown
% 0.23/0.40  % (3319)Termination phase: Property scanning
% 0.23/0.40  
% 0.23/0.40  % (3319)Memory used [KB]: 895
% 0.23/0.40  % (3319)Time elapsed: 0.004 s
% 0.23/0.40  % (3319)Instructions burned: 2 (million)
% 0.23/0.40  % (3319)------------------------------
% 0.23/0.40  % (3319)------------------------------
% 0.23/0.40  % (3322)Instruction limit reached!
% 0.23/0.40  % (3322)------------------------------
% 0.23/0.40  % (3322)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (3322)Termination reason: Unknown
% 0.23/0.40  % (3322)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (3322)Memory used [KB]: 5500
% 0.23/0.40  % (3322)Time elapsed: 0.005 s
% 0.23/0.40  % (3316)Instruction limit reached!
% 0.23/0.40  % (3316)------------------------------
% 0.23/0.40  % (3316)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.40  % (3322)Instructions burned: 3 (million)
% 0.23/0.40  % (3322)------------------------------
% 0.23/0.40  % (3322)------------------------------
% 0.23/0.40  % (3316)Termination reason: Unknown
% 0.23/0.40  % (3316)Termination phase: Saturation
% 0.23/0.40  
% 0.23/0.40  % (3316)Memory used [KB]: 5500
% 0.23/0.40  % (3316)Time elapsed: 0.007 s
% 0.23/0.40  % (3316)Instructions burned: 5 (million)
% 0.23/0.40  % (3316)------------------------------
% 0.23/0.40  % (3316)------------------------------
% 0.23/0.41  % (3320)First to succeed.
% 0.23/0.41  % (3317)Also succeeded, but the first one will report.
% 0.23/0.41  % (3320)Refutation found. Thanks to Tanya!
% 0.23/0.41  % SZS status Theorem for theBenchmark
% 0.23/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.41  % (3320)------------------------------
% 0.23/0.41  % (3320)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.41  % (3320)Termination reason: Refutation
% 0.23/0.41  
% 0.23/0.41  % (3320)Memory used [KB]: 5628
% 0.23/0.41  % (3320)Time elapsed: 0.017 s
% 0.23/0.41  % (3320)Instructions burned: 12 (million)
% 0.23/0.41  % (3320)------------------------------
% 0.23/0.41  % (3320)------------------------------
% 0.23/0.41  % (3314)Success in time 0.029 s
% 0.23/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------