TSTP Solution File: ANA091^1 by Vampire---4.8

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%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ANA091^1 : 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 : n028.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 18:40:27 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   76 (   9 unt;  15 typ;   0 def)
%            Number of atoms       :  576 ( 170 equ;   0 cnn)
%            Maximal formula atoms :   10 (   9 avg)
%            Number of connectives :  753 (  86   ~;  76   |;  48   &; 508   @)
%                                         (   2 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   44 (  44   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  15 usr;   9 con; 0-3 aty)
%                                         (   0  !!;   4  ??;   0 @@+;   0 @@-)
%            Number of variables   :  157 (   5   ^ 123   !;  25   ?; 157   :)
%                                         (   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_13,type,
    sK0: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).

thf(func_def_14,type,
    sK1: 'type/realax/real' > ( 'type/realax/real' > $o ) > 'type/realax/real' ).

thf(func_def_15,type,
    sK2: 'type/realax/real' > $o ).

thf(func_def_16,type,
    sK3: 'type/realax/real' ).

thf(func_def_17,type,
    sK4: 'type/realax/real' ).

thf(func_def_18,type,
    sK5: 'type/realax/real' ).

thf(func_def_20,type,
    sK7: 
      !>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).

thf(func_def_21,type,
    ph8: 
      !>[X0: $tType] : X0 ).

thf(func_def_22,type,
    sK9: 'type/realax/real' ).

thf(f136,plain,
    $false,
    inference(avatar_sat_refutation,[],[f110,f131,f135]) ).

thf(f135,plain,
    ( spl6_5
    | ~ spl6_6 ),
    inference(avatar_split_clause,[],[f134,f108,f105]) ).

thf(f105,plain,
    ( spl6_5
  <=> ! [X1: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
        | ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
          = $true ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

thf(f108,plain,
    ( spl6_6
  <=> ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

thf(f134,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) )
    | ~ spl6_6 ),
    inference(subsumption_resolution,[],[f133,f52]) ).

thf(f52,plain,
    'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ),
    inference(trivial_inequality_removal,[],[f49]) ).

thf(f49,plain,
    ( ( $true = $false )
    | ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK2 ) ) ),
    inference(superposition,[],[f44,f36]) ).

thf(f36,plain,
    ( $true
    = ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f26,plain,
    ( ( $true
     != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
    & ( $true
      = ( 'const/realax/real_le' @ sK5 @ sK4 ) )
    & ( $true
      = ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) )
    & ! [X4: 'type/realax/real'] :
        ( ( $true
          = ( 'const/realax/real_le' @ sK3 @ X4 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f16,f25]) ).

thf(f25,plain,
    ( ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
         != $true )
        & ( ( 'const/realax/real_le' @ X3 @ X2 )
          = $true )
        & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
          = $true )
        & ! [X4: 'type/realax/real'] :
            ( ( ( 'const/realax/real_le' @ X1 @ X4 )
              = $true )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             != $true ) ) )
   => ( ( $true
       != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) )
      & ( $true
        = ( 'const/realax/real_le' @ sK5 @ sK4 ) )
      & ( $true
        = ( 'const/sets/IN' @ 'type/realax/real' @ sK5 @ sK2 ) )
      & ! [X4: 'type/realax/real'] :
          ( ( $true
            = ( 'const/realax/real_le' @ sK3 @ X4 ) )
          | ( $true
           != ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

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

thf(f15,plain,
    ? [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 )
       != $true )
      & ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
        = $true )
      & ! [X4: 'type/realax/real'] :
          ( ( ( 'const/realax/real_le' @ X1 @ X4 )
            = $true )
          | ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
           != $true ) )
      & ( ( 'const/realax/real_le' @ X3 @ X2 )
        = $true ) ),
    inference(ennf_transformation,[],[f8]) ).

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

thf(f7,plain,
    ~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X2: 'type/realax/real',X3: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X3 @ X2 )
          & ! [X4: 'type/realax/real'] :
              ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             => ( 'const/realax/real_le' @ X1 @ X4 ) )
          & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ 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/realax/real_le' @ X3 @ X2 )
          & ! [X4: 'type/realax/real'] :
              ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
             => ( 'const/realax/real_le' @ X1 @ X4 ) )
          & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ 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/realax/real_le' @ X3 @ X2 )
        & ! [X4: 'type/realax/real'] :
            ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
           => ( 'const/realax/real_le' @ X1 @ X4 ) )
        & ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) )
     => ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_INF_LE_') ).

thf(f44,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
        = $false )
      | ( 'const/sets/EMPTY' @ ( X0 != X1 ) ) ),
    inference(equality_proxy_clausification,[],[f43]) ).

thf(f43,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
        = $false )
      | ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
        = $false ) ),
    inference(beta_eta_normalization,[],[f42]) ).

thf(f42,plain,
    ! [X0: $tType,X2: X0,X1: X0 > $o] :
      ( ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
        = $false )
      | ( ( ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 )
          @ X2 )
        = $false ) ),
    inference(pi_clausification,[],[f41]) ).

thf(f41,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ( ?? @ X0
          @ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
        = $false )
      | ( ( 'const/sets/EMPTY' @ ( X0 = X1 ) )
        = $false ) ),
    inference(not_proxy_clausification,[],[f40]) ).

thf(f40,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( $true
        = ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) )
      | ( ( ?? @ X0
          @ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
        = $false ) ),
    inference(binary_proxy_clausification,[],[f34]) ).

thf(f34,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ?? @ X0
        @ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
      = ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
    inference(cnf_transformation,[],[f10]) ).

thf(f10,plain,
    ! [X0: $tType,X1: X0 > $o] :
      ( ( ?? @ X0
        @ ^ [Y0: X0] : ( 'const/sets/IN' @ X0 @ Y0 @ X1 ) )
      = ( ~ ( 'const/sets/EMPTY' @ ( X0 = X1 ) ) ) ),
    inference(fool_elimination,[],[f9]) ).

thf(f9,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(f133,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) ) )
    | ~ spl6_6 ),
    inference(trivial_inequality_removal,[],[f132]) ).

thf(f132,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
        | ( $true
          = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( $true != $true ) )
    | ~ spl6_6 ),
    inference(superposition,[],[f27,f109]) ).

thf(f109,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
    | ~ spl6_6 ),
    inference(avatar_component_clause,[],[f108]) ).

thf(f27,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
      ( ( $true
       != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) )
      | ( $true
        = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
       != $true ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f24,plain,
    ! [X0: 'type/realax/real' > $o] :
      ( ! [X1: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
            = $true )
          & ( $true
           != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) )
      | ( ! [X3: 'type/realax/real'] :
            ( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 )
                = $true )
              & ( ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) )
               != $true ) )
            | ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) )
        & ! [X5: 'type/realax/real'] :
            ( ( $true
              = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
             != $true ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f23,f22]) ).

thf(f22,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/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
          = $true )
        & ( $true
         != ( 'const/realax/real_le' @ X1 @ ( sK0 @ X1 @ X0 ) ) ) ) ),
    introduced(choice_axiom,[]) ).

thf(f23,plain,
    ! [X0: 'type/realax/real' > $o,X3: 'type/realax/real'] :
      ( ? [X4: 'type/realax/real'] :
          ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
            = $true )
          & ( $true
           != ( 'const/realax/real_le' @ X3 @ X4 ) ) )
     => ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK1 @ X3 @ X0 ) @ X0 )
          = $true )
        & ( ( 'const/realax/real_le' @ X3 @ ( sK1 @ X3 @ X0 ) )
         != $true ) ) ),
    introduced(choice_axiom,[]) ).

thf(f21,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 ) )
      | ( ! [X3: 'type/realax/real'] :
            ( ? [X4: 'type/realax/real'] :
                ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ X0 )
                  = $true )
                & ( $true
                 != ( 'const/realax/real_le' @ X3 @ X4 ) ) )
            | ( ( 'const/realax/real_le' @ X3 @ ( 'const/sets/inf' @ X0 ) )
              = $true ) )
        & ! [X5: 'type/realax/real'] :
            ( ( $true
              = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
             != $true ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(rectify,[],[f20]) ).

thf(f20,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 ) )
      | ( ! [X4: 'type/realax/real'] :
            ( ? [X5: 'type/realax/real'] :
                ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true )
                & ( $true
                 != ( 'const/realax/real_le' @ X4 @ X5 ) ) )
            | ( $true
              = ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
        & ! [X3: 'type/realax/real'] :
            ( ( $true
              = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             != $true ) ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
    inference(flattening,[],[f19]) ).

thf(f19,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 ) ) )
            | ( $true
              = ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
        & ! [X3: 'type/realax/real'] :
            ( ( $true
              = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) )
            | ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
             != $true ) ) )
      | ! [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 ) ) ),
    inference(ennf_transformation,[],[f12]) ).

thf(f12,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 ) ) )
     => ( ! [X4: 'type/realax/real'] :
            ( ! [X5: 'type/realax/real'] :
                ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
                  = $true )
               => ( $true
                  = ( 'const/realax/real_le' @ X4 @ X5 ) ) )
           => ( $true
              = ( 'const/realax/real_le' @ X4 @ ( 'const/sets/inf' @ X0 ) ) ) )
        & ! [X3: 'type/realax/real'] :
            ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 )
              = $true )
           => ( $true
              = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X3 ) ) ) ) ),
    inference(fool_elimination,[],[f11]) ).

thf(f11,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,[],[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' @ 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/sandbox2/benchmark/theBenchmark.p','thm/sets/INF_') ).

thf(f131,plain,
    ~ spl6_5,
    inference(avatar_contradiction_clause,[],[f130]) ).

thf(f130,plain,
    ( $false
    | ~ spl6_5 ),
    inference(subsumption_resolution,[],[f127,f37]) ).

thf(f37,plain,
    ( $true
    = ( 'const/realax/real_le' @ sK5 @ sK4 ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f127,plain,
    ( ( $true
     != ( 'const/realax/real_le' @ sK5 @ sK4 ) )
    | ~ spl6_5 ),
    inference(trivial_inequality_removal,[],[f123]) ).

thf(f123,plain,
    ( ( $true
     != ( 'const/realax/real_le' @ sK5 @ sK4 ) )
    | ( $true != $true )
    | ~ spl6_5 ),
    inference(superposition,[],[f120,f36]) ).

thf(f120,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) )
        | ( ( 'const/realax/real_le' @ X0 @ sK4 )
         != $true ) )
    | ~ spl6_5 ),
    inference(trivial_inequality_removal,[],[f114]) ).

thf(f114,plain,
    ( ! [X0: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ X0 @ sK4 )
         != $true )
        | ( $true != $true )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK2 ) ) )
    | ~ spl6_5 ),
    inference(superposition,[],[f90,f106]) ).

thf(f106,plain,
    ( ! [X1: 'type/realax/real'] :
        ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
          = $true )
        | ( $true
         != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) ) )
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f105]) ).

thf(f90,plain,
    ! [X0: 'type/realax/real'] :
      ( ( $true
       != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) )
      | ( ( 'const/realax/real_le' @ X0 @ sK4 )
       != $true ) ),
    inference(trivial_inequality_removal,[],[f89]) ).

thf(f89,plain,
    ! [X0: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ X0 @ sK4 )
       != $true )
      | ( $true != $true )
      | ( $true
       != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X0 ) ) ),
    inference(superposition,[],[f38,f33]) ).

thf(f33,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' @ X1 @ X2 )
       != $true )
      | ( ( 'const/realax/real_le' @ X0 @ X1 )
       != $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,[],[f14]) ).

thf(f14,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,[],[f13]) ).

thf(f13,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(f38,plain,
    ( $true
   != ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ sK4 ) ),
    inference(cnf_transformation,[],[f26]) ).

thf(f110,plain,
    ( spl6_5
    | spl6_6 ),
    inference(avatar_split_clause,[],[f103,f108,f105]) ).

thf(f103,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
      | ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
        = $true ) ),
    inference(subsumption_resolution,[],[f102,f52]) ).

thf(f102,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
        = $true )
      | ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true ) ),
    inference(trivial_inequality_removal,[],[f100]) ).

thf(f100,plain,
    ! [X0: 'type/realax/real',X1: 'type/realax/real'] :
      ( ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK2 ) )
      | ( $true != $true )
      | ( ( 'const/realax/real_le' @ sK3 @ ( sK0 @ X0 @ sK2 ) )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK2 ) )
      | ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK2 ) @ X1 )
        = $true ) ),
    inference(superposition,[],[f35,f30]) ).

thf(f30,plain,
    ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real',X5: 'type/realax/real'] :
      ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( sK0 @ X1 @ X0 ) @ X0 )
        = $true )
      | ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
      | ( ( 'const/sets/IN' @ 'type/realax/real' @ X5 @ X0 )
       != $true )
      | ( $true
        = ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X5 ) ) ),
    inference(cnf_transformation,[],[f24]) ).

thf(f35,plain,
    ! [X4: 'type/realax/real'] :
      ( ( $true
       != ( 'const/sets/IN' @ 'type/realax/real' @ X4 @ sK2 ) )
      | ( $true
        = ( 'const/realax/real_le' @ sK3 @ X4 ) ) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : ANA091^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 07:46:23 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a TH1_THM_EQU_NAR problem
% 0.15/0.35  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
% 0.15/0.37  % (4163)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.37  % (4157)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38  % (4161)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)
% 0.15/0.38  % (4158)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)
% 0.15/0.38  % (4160)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38  % (4159)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)
% 0.15/0.38  % (4162)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)
% 0.15/0.38  % (4164)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)
% 0.15/0.38  % (4160)Instruction limit reached!
% 0.15/0.38  % (4160)------------------------------
% 0.15/0.38  % (4160)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (4160)Termination reason: Unknown
% 0.15/0.38  % (4161)Instruction limit reached!
% 0.15/0.38  % (4161)------------------------------
% 0.15/0.38  % (4161)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (4161)Termination reason: Unknown
% 0.15/0.38  % (4161)Termination phase: Property scanning
% 0.15/0.38  
% 0.15/0.38  % (4161)Memory used [KB]: 895
% 0.15/0.38  % (4161)Time elapsed: 0.004 s
% 0.15/0.38  % (4161)Instructions burned: 3 (million)
% 0.15/0.38  % (4161)------------------------------
% 0.15/0.38  % (4161)------------------------------
% 0.15/0.38  % (4160)Termination phase: Unused predicate definition removal
% 0.15/0.38  
% 0.15/0.38  % (4160)Memory used [KB]: 895
% 0.15/0.38  % (4160)Time elapsed: 0.004 s
% 0.15/0.38  % (4160)Instructions burned: 2 (million)
% 0.15/0.38  % (4160)------------------------------
% 0.15/0.38  % (4160)------------------------------
% 0.15/0.38  % (4164)Instruction limit reached!
% 0.15/0.38  % (4164)------------------------------
% 0.15/0.38  % (4164)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (4164)Termination reason: Unknown
% 0.15/0.38  % (4164)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (4164)Memory used [KB]: 895
% 0.15/0.38  % (4164)Time elapsed: 0.005 s
% 0.15/0.38  % (4164)Instructions burned: 3 (million)
% 0.15/0.38  % (4164)------------------------------
% 0.15/0.38  % (4164)------------------------------
% 0.15/0.38  % (4157)First to succeed.
% 0.15/0.38  % (4158)Instruction limit reached!
% 0.15/0.38  % (4158)------------------------------
% 0.15/0.38  % (4158)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (4158)Termination reason: Unknown
% 0.15/0.38  % (4158)Termination phase: Saturation
% 0.15/0.38  
% 0.15/0.38  % (4158)Memory used [KB]: 5500
% 0.15/0.38  % (4158)Time elapsed: 0.007 s
% 0.15/0.38  % (4158)Instructions burned: 5 (million)
% 0.15/0.38  % (4158)------------------------------
% 0.15/0.38  % (4158)------------------------------
% 0.15/0.38  % (4163)Instruction limit reached!
% 0.15/0.38  % (4163)------------------------------
% 0.15/0.38  % (4163)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38  % (4163)Termination reason: Unknown
% 0.15/0.39  % (4163)Termination phase: Saturation
% 0.15/0.39  
% 0.15/0.39  % (4163)Memory used [KB]: 5628
% 0.15/0.39  % (4163)Time elapsed: 0.017 s
% 0.15/0.39  % (4163)Instructions burned: 18 (million)
% 0.15/0.39  % (4163)------------------------------
% 0.15/0.39  % (4163)------------------------------
% 0.15/0.39  % (4157)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (4157)------------------------------
% 0.15/0.39  % (4157)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39  % (4157)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (4157)Memory used [KB]: 5628
% 0.15/0.39  % (4157)Time elapsed: 0.017 s
% 0.15/0.39  % (4157)Instructions burned: 16 (million)
% 0.15/0.39  % (4157)------------------------------
% 0.15/0.39  % (4157)------------------------------
% 0.15/0.39  % (4156)Success in time 0.03 s
% 0.15/0.39  % Vampire---4.8 exiting
%------------------------------------------------------------------------------