TSTP Solution File: ANA088^1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA088^1 : TPTP v8.1.2. 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 : n005.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 04:31:07 EDT 2024

% Result   : Theorem 0.15s 0.35s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  115 (   3 unt;  14 typ;   0 def)
%            Number of atoms       :  982 ( 269 equ;   0 cnn)
%            Maximal formula atoms :   14 (   9 avg)
%            Number of connectives : 1228 ( 157   ~; 180   |;  55   &; 797   @)
%                                         (   9 <=>;  30  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   47 (  47   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   23 (  20 usr;  13 con; 0-3 aty)
%            Number of variables   :  192 (   0   ^ 162   !;  26   ?; 192   :)
%                                         (   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/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_12,type,
    sK4: 'type/realax/real' ).

thf(func_def_13,type,
    sK5: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_15,type,
    ph7: 
      !>[X0: $tType] : X0 ).

thf(func_def_16,type,
    sK8: 'type/realax/real' ).

thf(f236,plain,
    $false,
    inference(avatar_sat_refutation,[],[f53,f94,f99,f107,f113,f141,f178,f193,f201,f203,f235]) ).

thf(f235,plain,
    ( spl6_11
    | ~ spl6_12 ),
    inference(avatar_split_clause,[],[f234,f111,f105]) ).

thf(f105,plain,
    ( spl6_11
  <=> ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).

thf(f111,plain,
    ( spl6_12
  <=> ! [X1: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).

thf(f234,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_12 ),
    inference(trivial_inequality_removal,[],[f232]) ).

thf(f232,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
          = $true )
        | ( $true != $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_12 ),
    inference(superposition,[],[f39,f112]) ).

thf(f112,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
          = $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_12 ),
    inference(avatar_component_clause,[],[f111]) ).

thf(f39,plain,
    ! [X3: 'type/realax/real'] :
      ( ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ X3 )
        = $true ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f26,plain,
    ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
    & ! [X3: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
        | ( ( ( 'const/realax/real_le' @ X3 @ sK4 )
            = $true )
          & ( ( 'const/realax/real_le' @ sK3 @ X3 )
            = $true ) ) )
    & ( ( $true
       != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
      | ( $true
       != ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f18,f25]) ).

thf(f25,plain,
    ( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
        ( ( '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 @ X2 )
                = $true )
              & ( ( 'const/realax/real_le' @ X1 @ X3 )
                = $true ) ) )
        & ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
           != $true )
          | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
           != $true ) ) )
   => ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) )
      & ! [X3: 'type/realax/real'] :
          ( ( $true
           != ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
          | ( ( ( 'const/realax/real_le' @ X3 @ sK4 )
              = $true )
            & ( ( 'const/realax/real_le' @ sK3 @ X3 )
              = $true ) ) )
      & ( ( $true
         != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
        | ( $true
         != ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f18,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( '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 @ X2 )
              = $true )
            & ( ( 'const/realax/real_le' @ X1 @ X3 )
              = $true ) ) )
      & ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
         != $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
         != $true ) ) ),
    inference(flattening,[],[f17]) ).

thf(f17,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real'] :
      ( ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
         != $true )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
         != $true ) )
      & ! [X3: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
           != $true )
          | ( ( ( 'const/realax/real_le' @ X3 @ X2 )
              = $true )
            & ( ( 'const/realax/real_le' @ X1 @ X3 )
              = $true ) ) )
      & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
    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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
                = $true )
             => ( ( ( 'const/realax/real_le' @ X3 @ X2 )
                  = $true )
                & ( ( 'const/realax/real_le' @ X1 @ X3 )
                  = $true ) ) )
          & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
       => ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
            = $true )
          & ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ 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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             => ( ( 'const/realax/real_le' @ X1 @ X3 )
                & ( 'const/realax/real_le' @ X3 @ X2 ) ) )
          & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
       => ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
          & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
    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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             => ( ( 'const/realax/real_le' @ X1 @ X3 )
                & ( 'const/realax/real_le' @ X3 @ X2 ) ) )
          & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
       => ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
          & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
    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/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
           => ( ( 'const/realax/real_le' @ X1 @ X3 )
              & ( 'const/realax/real_le' @ X3 @ X2 ) ) )
        & ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
     => ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ X0 ) )
        & ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/REAL_INF_BOUNDS_') ).

thf(f203,plain,
    ( spl6_9
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f202,f89,f97]) ).

thf(f97,plain,
    ( spl6_9
  <=> ! [X1: 'type/realax/real'] :
        ( ( $true
         != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

thf(f89,plain,
    ( spl6_7
  <=> ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

thf(f202,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_7 ),
    inference(subsumption_resolution,[],[f199,f41]) ).

thf(f41,plain,
    'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
    inference(cnf_transformation,[],[f26]) ).

thf(f199,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true ) )
    | ~ spl6_7 ),
    inference(trivial_inequality_removal,[],[f197]) ).

thf(f197,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ ( sK0 @ X0 @ sK2 ) )
         != $true )
        | ( $true != $true )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_7 ),
    inference(superposition,[],[f34,f90]) ).

thf(f90,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f89]) ).

thf(f34,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
       != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( $true
        = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
      | ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
       != $true ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f24,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ! [X1: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
             != $true ) )
        & ! [X2: 'type/realax/real'] :
            ( ( ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
               != $true )
              & ( $true
                = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) ) )
            | ( $true
              = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ! [X4: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
           != $true )
          & ( $true
            = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23,f22]) ).

thf(f22,plain,
    ! [X0: 'type/realax/real' > $o,X2: 'type/realax/real'] :
      ( ? [X3: 'type/realax/real'] :
          ( ( $true
           != ( 'const/realax/real_le' @ X2 @ X3 ) )
          & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
            = $true ) )
     => ( ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
         != $true )
        & ( $true
          = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f23,plain,
    ! [X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ? [X5: 'type/realax/real'] :
          ( ( $true
           != ( 'const/realax/real_le' @ X4 @ X5 ) )
          & ( $true
            = ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) )
     => ( ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
         != $true )
        & ( $true
          = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f21,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ! [X1: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
             != $true ) )
        & ! [X2: 'type/realax/real'] :
            ( ? [X3: 'type/realax/real'] :
                ( ( $true
                 != ( 'const/realax/real_le' @ X2 @ X3 ) )
                & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
                  = $true ) )
            | ( $true
              = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ! [X4: 'type/realax/real'] :
        ? [X5: 'type/realax/real'] :
          ( ( $true
           != ( 'const/realax/real_le' @ X4 @ X5 ) )
          & ( $true
            = ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 ) ) ) ),
    inference(rectify,[],[f16]) ).

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

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

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

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

thf(f3,axiom,
    ! [X0: 'type/realax/real' > $o] :
      ( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
        & ? [X1: 'type/realax/real'] :
          ! [X2: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
           => ( 'const/realax/real_le' @ X1 @ X2 ) ) )
     => ( ! [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 ) ) )
        & ! [X1: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
           => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/INF_') ).

thf(f201,plain,
    ( spl6_8
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f200,f89,f92]) ).

thf(f92,plain,
    ( spl6_8
  <=> ! [X1: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
        | ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

thf(f200,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
    | ~ spl6_7 ),
    inference(subsumption_resolution,[],[f198,f41]) ).

thf(f198,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
    | ~ spl6_7 ),
    inference(trivial_inequality_removal,[],[f196]) ).

thf(f196,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( $true != $true )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) )
    | ~ spl6_7 ),
    inference(superposition,[],[f36,f90]) ).

thf(f36,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' @ ( 'const/sets/inf' @ X0 ) @ X1 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
       != $true ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f193,plain,
    ( spl6_2
    | ~ spl6_9
    | ~ spl6_11 ),
    inference(avatar_split_clause,[],[f190,f105,f97,f50]) ).

thf(f50,plain,
    ( spl6_2
  <=> ( $true
      = ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

thf(f190,plain,
    ( ( $true
      = ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
    | ~ spl6_9
    | ~ spl6_11 ),
    inference(trivial_inequality_removal,[],[f189]) ).

thf(f189,plain,
    ( ( $true != $true )
    | ( $true
      = ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
    | ~ spl6_9
    | ~ spl6_11 ),
    inference(duplicate_literal_removal,[],[f188]) ).

thf(f188,plain,
    ( ( $true
      = ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
    | ( $true != $true )
    | ( $true
      = ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) )
    | ~ spl6_9
    | ~ spl6_11 ),
    inference(superposition,[],[f98,f106]) ).

thf(f106,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
          = $true )
        | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_11 ),
    inference(avatar_component_clause,[],[f105]) ).

thf(f98,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( $true
         != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
        | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
          = $true ) )
    | ~ spl6_9 ),
    inference(avatar_component_clause,[],[f97]) ).

thf(f178,plain,
    ( spl6_1
    | ~ spl6_8 ),
    inference(avatar_contradiction_clause,[],[f177]) ).

thf(f177,plain,
    ( $false
    | spl6_1
    | ~ spl6_8 ),
    inference(subsumption_resolution,[],[f175,f41]) ).

thf(f175,plain,
    ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
    | spl6_1
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f171]) ).

thf(f171,plain,
    ( ( $true != $true )
    | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
    | spl6_1
    | ~ spl6_8 ),
    inference(superposition,[],[f162,f42]) ).

thf(f42,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true
        = ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) )
      | ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ),
    inference(cnf_transformation,[],[f30]) ).

thf(f30,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
        | ! [X2: X0] :
            ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
           != $true ) )
      & ( ( $true
          = ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) )
        | ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f29]) ).

thf(f29,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ? [X3: X0] :
          ( $true
          = ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
     => ( $true
        = ( 'const/sets/IN' @ X0 @ ( sK5 @ X0 @ X1 ) @ X1 ) ) ),
    introduced(choice_axiom,[]) ).

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

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

thf(f14,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( 'const/sets/EMPTY' @ ( X0 != X1 ) )
    <=> ? [X2: X0] :
          ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
          = $true ) ),
    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/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/sets/MEMBER_NOT_EMPTY_') ).

thf(f162,plain,
    ( ! [X0: 'type/realax/real'] :
        ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
    | spl6_1
    | ~ spl6_8 ),
    inference(subsumption_resolution,[],[f160,f40]) ).

thf(f40,plain,
    ! [X3: 'type/realax/real'] :
      ( ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ sK2 ) )
      | ( ( 'const/realax/real_le' @ X3 @ sK4 )
        = $true ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f160,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( $true
         != ( 'const/realax/real_le' @ X0 @ sK4 ) ) )
    | spl6_1
    | ~ spl6_8 ),
    inference(trivial_inequality_removal,[],[f152]) ).

thf(f152,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/realax/real_le' @ X0 @ sK4 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( $true != $true ) )
    | spl6_1
    | ~ spl6_8 ),
    inference(superposition,[],[f76,f93]) ).

thf(f93,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) )
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f92]) ).

thf(f76,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( $true
         != ( 'const/realax/real_le' @ X0 @ sK4 ) ) )
    | spl6_1 ),
    inference(trivial_inequality_removal,[],[f75]) ).

thf(f75,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( $true
         != ( 'const/realax/real_le' @ X0 @ sK4 ) )
        | ( $true != $true ) )
    | spl6_1 ),
    inference(superposition,[],[f48,f37]) ).

thf(f37,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real',X1: '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(cnf_transformation,[],[f20]) ).

thf(f20,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 @ X2 )
        = $true )
      | ( ( 'const/realax/real_le' @ X0 @ X1 )
       != $true ) ),
    inference(flattening,[],[f19]) ).

thf(f19,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' @ X1 @ X2 )
        & ( 'const/realax/real_le' @ X0 @ X1 ) )
     => ( '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' @ X1 @ X2 )
        & ( 'const/realax/real_le' @ X0 @ X1 ) )
     => ( 'const/realax/real_le' @ X0 @ X2 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.qV3j58wWel/Vampire---4.8_3631','thm/realax/REAL_LE_TRANS_') ).

thf(f48,plain,
    ( ( $true
     != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
    | spl6_1 ),
    inference(avatar_component_clause,[],[f46]) ).

thf(f46,plain,
    ( spl6_1
  <=> ( $true
      = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

thf(f141,plain,
    ( ~ spl6_7
    | ~ spl6_10 ),
    inference(avatar_contradiction_clause,[],[f140]) ).

thf(f140,plain,
    ( $false
    | ~ spl6_7
    | ~ spl6_10 ),
    inference(trivial_inequality_removal,[],[f138]) ).

thf(f138,plain,
    ( ( $true != $true )
    | ~ spl6_7
    | ~ spl6_10 ),
    inference(superposition,[],[f103,f90]) ).

thf(f103,plain,
    ( ! [X1: 'type/realax/real'] :
        ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
    | ~ spl6_10 ),
    inference(avatar_component_clause,[],[f102]) ).

thf(f102,plain,
    ( spl6_10
  <=> ! [X1: 'type/realax/real'] :
        ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).

thf(f113,plain,
    ( spl6_7
    | spl6_12 ),
    inference(avatar_split_clause,[],[f109,f111,f89]) ).

thf(f109,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true ) ),
    inference(subsumption_resolution,[],[f82,f41]) ).

thf(f82,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
    inference(trivial_inequality_removal,[],[f79]) ).

thf(f79,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ sK2 ) @ sK2 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
    inference(superposition,[],[f39,f31]) ).

thf(f31,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
      | ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( $true
        = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f107,plain,
    ( spl6_10
    | spl6_11 ),
    inference(avatar_split_clause,[],[f100,f105,f102]) ).

thf(f100,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) ) ),
    inference(subsumption_resolution,[],[f84,f41]) ).

thf(f84,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
    inference(trivial_inequality_removal,[],[f77]) ).

thf(f77,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK1 @ X1 @ sK2 ) ) )
      | ( $true != $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true ) ),
    inference(superposition,[],[f39,f32]) ).

thf(f32,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X2 @ X0 ) @ X0 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/realax/real_le' @ X4 @ ( sK1 @ X4 @ X0 ) )
       != $true )
      | ( $true
        = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f99,plain,
    ( spl6_9
    | spl6_7 ),
    inference(avatar_split_clause,[],[f95,f89,f97]) ).

thf(f95,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true ) ),
    inference(subsumption_resolution,[],[f85,f41]) ).

thf(f85,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) ),
    inference(trivial_inequality_removal,[],[f80]) ).

thf(f80,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/inf' @ sK2 ) )
        = $true )
      | ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ sK2 ) ) ) ),
    inference(superposition,[],[f39,f33]) ).

thf(f33,plain,
    ! [X2: 'type/realax/real',X0: 'type/realax/real' > $o,X4: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
      | ( ( 'const/realax/real_le' @ X2 @ ( sK0 @ X2 @ X0 ) )
       != $true )
      | ( $true
        = ( 'const/realax/real_le' @ X2 @ ( 'const/sets/inf' @ X0 ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f94,plain,
    ( spl6_7
    | spl6_8 ),
    inference(avatar_split_clause,[],[f87,f92,f89]) ).

thf(f87,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( $true
        = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) ) ),
    inference(subsumption_resolution,[],[f86,f41]) ).

thf(f86,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( $true
        = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true )
      | ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) ),
    inference(trivial_inequality_removal,[],[f78]) ).

thf(f78,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
        = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 ) )
      | ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK1 @ X0 @ sK2 ) )
        = $true ) ),
    inference(superposition,[],[f39,f35]) ).

thf(f35,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X4: 'type/realax/real'] :
      ( ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X4 @ X0 ) @ X0 ) )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
       != $true )
      | ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f53,plain,
    ( ~ spl6_1
    | ~ spl6_2 ),
    inference(avatar_split_clause,[],[f38,f50,f46]) ).

thf(f38,plain,
    ( ( $true
     != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
    | ( $true
     != ( 'const/realax/real_le' @ sK3 @ ( 'const/sets/inf' @ sK2 ) ) ) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : ANA088^1 : TPTP v8.1.2. Released v7.0.0.
% 0.05/0.11  % 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
% 0.10/0.31  % Computer : n005.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 15:30:53 EDT 2024
% 0.15/0.31  % CPUTime    : 
% 0.15/0.31  This is a TH1_THM_EQU_NAR problem
% 0.15/0.31  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/tmp/tmp.qV3j58wWel/Vampire---4.8_3631
% 0.15/0.33  % (3742)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.33  % (3741)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 Vampire---4 for (2999ds/27Mi)
% 0.15/0.33  % (3744)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.15/0.33  % (3739)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.15/0.33  % (3743)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.15/0.33  % (3742)Instruction limit reached!
% 0.15/0.33  % (3742)------------------------------
% 0.15/0.33  % (3742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33  % (3742)Termination reason: Unknown
% 0.15/0.33  % (3742)Termination phase: Saturation
% 0.15/0.33  
% 0.15/0.33  % (3745)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.15/0.33  % (3742)Memory used [KB]: 5500
% 0.15/0.33  % (3743)Instruction limit reached!
% 0.15/0.33  % (3743)------------------------------
% 0.15/0.33  % (3743)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33  % (3743)Termination reason: Unknown
% 0.15/0.33  % (3742)Time elapsed: 0.003 s
% 0.15/0.33  % (3743)Termination phase: shuffling
% 0.15/0.33  % (3742)Instructions burned: 3 (million)
% 0.15/0.33  
% 0.15/0.33  % (3742)------------------------------
% 0.15/0.33  % (3742)------------------------------
% 0.15/0.33  % (3743)Memory used [KB]: 895
% 0.15/0.33  % (3743)Time elapsed: 0.002 s
% 0.15/0.33  % (3743)Instructions burned: 2 (million)
% 0.15/0.33  % (3743)------------------------------
% 0.15/0.33  % (3743)------------------------------
% 0.15/0.33  % (3746)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.15/0.34  % (3746)Instruction limit reached!
% 0.15/0.34  % (3746)------------------------------
% 0.15/0.34  % (3746)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34  % (3746)Termination reason: Unknown
% 0.15/0.34  % (3746)Termination phase: Saturation
% 0.15/0.34  
% 0.15/0.34  % (3746)Memory used [KB]: 5500
% 0.15/0.34  % (3746)Time elapsed: 0.004 s
% 0.15/0.34  % (3746)Instructions burned: 3 (million)
% 0.15/0.34  % (3746)------------------------------
% 0.15/0.34  % (3746)------------------------------
% 0.15/0.34  % (3740)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 Vampire---4 for (2999ds/4Mi)
% 0.15/0.34  % (3740)Instruction limit reached!
% 0.15/0.34  % (3740)------------------------------
% 0.15/0.34  % (3740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34  % (3740)Termination reason: Unknown
% 0.15/0.34  % (3740)Termination phase: Saturation
% 0.15/0.34  
% 0.15/0.34  % (3740)Memory used [KB]: 5500
% 0.15/0.34  % (3740)Time elapsed: 0.003 s
% 0.15/0.34  % (3740)Instructions burned: 4 (million)
% 0.15/0.34  % (3740)------------------------------
% 0.15/0.34  % (3740)------------------------------
% 0.15/0.34  % (3745)Instruction limit reached!
% 0.15/0.34  % (3745)------------------------------
% 0.15/0.34  % (3745)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34  % (3745)Termination reason: Unknown
% 0.15/0.34  % (3745)Termination phase: Saturation
% 0.15/0.34  
% 0.15/0.34  % (3745)Memory used [KB]: 5628
% 0.15/0.34  % (3745)Time elapsed: 0.012 s
% 0.15/0.34  % (3745)Instructions burned: 18 (million)
% 0.15/0.34  % (3745)------------------------------
% 0.15/0.34  % (3745)------------------------------
% 0.15/0.34  % (3747)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 Vampire---4 for (2999ds/37Mi)
% 0.15/0.34  % (3741)Instruction limit reached!
% 0.15/0.34  % (3741)------------------------------
% 0.15/0.34  % (3741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34  % (3741)Termination reason: Unknown
% 0.15/0.34  % (3741)Termination phase: Saturation
% 0.15/0.34  
% 0.15/0.34  % (3741)Memory used [KB]: 5756
% 0.15/0.34  % (3741)Time elapsed: 0.016 s
% 0.15/0.34  % (3741)Instructions burned: 27 (million)
% 0.15/0.34  % (3741)------------------------------
% 0.15/0.34  % (3741)------------------------------
% 0.15/0.35  % (3744)First to succeed.
% 0.15/0.35  % (3748)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on Vampire---4 for (2999ds/15Mi)
% 0.15/0.35  % (3744)Refutation found. Thanks to Tanya!
% 0.15/0.35  % SZS status Theorem for Vampire---4
% 0.15/0.35  % SZS output start Proof for Vampire---4
% See solution above
% 0.15/0.35  % (3744)------------------------------
% 0.15/0.35  % (3744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.35  % (3744)Termination reason: Refutation
% 0.15/0.35  
% 0.15/0.35  % (3744)Memory used [KB]: 5628
% 0.15/0.35  % (3744)Time elapsed: 0.022 s
% 0.15/0.35  % (3744)Instructions burned: 33 (million)
% 0.15/0.35  % (3744)------------------------------
% 0.15/0.35  % (3744)------------------------------
% 0.15/0.35  % (3738)Success in time 0.033 s
% 0.15/0.35  % Vampire---4.8 exiting
%------------------------------------------------------------------------------