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Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : NUM547+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:09:07 AM UTC 2026

% Result   : Theorem 8.75s 3.85s
% Output   : Refutation 9.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   19 (  10 unt;   0 typ;   5 def)
%            Number of atoms       :  248 (  46 equ;   0 cnn)
%            Maximal formula atoms :   67 (  13 avg)
%            Number of connectives :  849 (  61   ~;  65   |; 109   &; 564   @)
%                                         (   0 <=>;  50  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   41 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  14 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (   4   ^;  51   !;   8   ?;  68   :)
%                                         (   0  !>;   0  ?*;   0  @-;   5  @+)

% Comments : 
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
    slcrc0: $i ).

thf(aSet0_decl,type,
    aSet0: $i > $o ).

thf(aElementOf0_decl,type,
    aElementOf0: $i > $i > $o ).

thf(aSubsetOf0_decl,type,
    aSubsetOf0: $i > $i > $o ).

thf(slbdtsldtrb0_decl,type,
    slbdtsldtrb0: $i > $i > $i ).

thf(sbrdtbr0_decl,type,
    sbrdtbr0: $i > $i ).

thf(xS_decl,type,
    xS: $i ).

thf(xk_decl,type,
    xk: $i ).

thf(xT_decl,type,
    xT: $i ).

thf(sk1_decl,type,
    sk1: $i > $i ).

thf(sk18_decl,type,
    sk18: $i > $i ).

thf(sk19_decl,type,
    sk19: $i > $i ).

thf(sk20_decl,type,
    sk20: $i > $i ).

thf(sk21_decl,type,
    sk21: $i ).

thf(sk1_def,definition,
    ( sk1
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( A @ ( B @ aElementOf0 ) )
           => ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).

thf(sk18_def,definition,
    ( sk18
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( A @ ( B @ aElementOf0 ) )
           => ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).

thf(sk19_def,definition,
    ( sk19
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( A @ ( B @ aElementOf0 ) )
           => ( xT @ ( B @ aElementOf0 ) ) ) ) ) ).

thf(sk20_def,definition,
    ( sk20
    = ( ^ [A: $i] :
        @+[B: $i] :
          ~ ( ( A @ ( B @ aElementOf0 ) )
           => ( xS @ ( B @ aElementOf0 ) ) ) ) ) ).

thf(sk21_def,definition,
    ( sk21
    = ( @+[A: $i] : ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) ) ) ).

thf(52,axiom,
    ( ~ ( ! [A: $i] :
            ( ( ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( ( xS @ ( A @ aSubsetOf0 ) )
                  | ( ! [B: $i] :
                        ( ( A @ ( B @ aElementOf0 ) )
                       => ( xS @ ( B @ aElementOf0 ) ) )
                    & ( A @ aSet0 ) ) ) )
             => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
            & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
             => ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( xS @ ( A @ aSubsetOf0 ) )
                & ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xS @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
       => ( ( ( xk @ ( xS @ slbdtsldtrb0 ) )
            = slcrc0 )
          | ~ ? [A: $i] : ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ ( xk @ ( xS @ slbdtsldtrb0 ) @ aSubsetOf0 ) )
    & ! [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
       => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
    & ! [A: $i] :
        ( ( ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( ( xT @ ( A @ aSubsetOf0 ) )
              | ( ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xT @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
         => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
        & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
         => ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( xT @ ( A @ aSubsetOf0 ) )
            & ! [B: $i] :
                ( ( A @ ( B @ aElementOf0 ) )
               => ( xT @ ( B @ aElementOf0 ) ) )
            & ( A @ aSet0 ) ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ aSet0 )
    & ! [A: $i] :
        ( ( ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( ( xS @ ( A @ aSubsetOf0 ) )
              | ( ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xS @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
         => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
        & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
         => ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( xS @ ( A @ aSubsetOf0 ) )
            & ! [B: $i] :
                ( ( A @ ( B @ aElementOf0 ) )
               => ( xS @ ( B @ aElementOf0 ) ) )
            & ( A @ aSet0 ) ) ) )
    & ( xk @ ( xS @ slbdtsldtrb0 ) @ aSet0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).

thf(341,plain,
    ( ~ ( ! [A: $i] :
            ( ( ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( ( xS @ ( A @ aSubsetOf0 ) )
                  | ( ! [B: $i] :
                        ( ( A @ ( B @ aElementOf0 ) )
                       => ( xS @ ( B @ aElementOf0 ) ) )
                    & ( A @ aSet0 ) ) ) )
             => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
            & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
             => ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( xS @ ( A @ aSubsetOf0 ) )
                & ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xS @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
       => ( ( ( xk @ ( xS @ slbdtsldtrb0 ) )
            = slcrc0 )
          | ~ ? [A: $i] : ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ ( xk @ ( xS @ slbdtsldtrb0 ) @ aSubsetOf0 ) )
    & ! [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
       => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
    & ! [A: $i] :
        ( ( ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( ( xT @ ( A @ aSubsetOf0 ) )
              | ( ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xT @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
         => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
        & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
         => ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( xT @ ( A @ aSubsetOf0 ) )
            & ! [B: $i] :
                ( ( A @ ( B @ aElementOf0 ) )
               => ( xT @ ( B @ aElementOf0 ) ) )
            & ( A @ aSet0 ) ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ aSet0 )
    & ! [A: $i] :
        ( ( ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( ( xS @ ( A @ aSubsetOf0 ) )
              | ( ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xS @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
         => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
        & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
         => ( ( ( A @ sbrdtbr0 )
              = xk )
            & ( xS @ ( A @ aSubsetOf0 ) )
            & ! [B: $i] :
                ( ( A @ ( B @ aElementOf0 ) )
               => ( xS @ ( B @ aElementOf0 ) ) )
            & ( A @ aSet0 ) ) ) )
    & ( xk @ ( xS @ slbdtsldtrb0 ) @ aSet0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(342,plain,
    ( ~ ( ( ! [A: $i] :
              ( ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( ( xS @ ( A @ aSubsetOf0 ) )
                  | ( ! [B: $i] :
                        ( ( A @ ( B @ aElementOf0 ) )
                       => ( xS @ ( B @ aElementOf0 ) ) )
                    & ( A @ aSet0 ) ) ) )
             => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
          & ! [A: $i] :
              ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
             => ( ( ( A @ sbrdtbr0 )
                  = xk )
                & ( xS @ ( A @ aSubsetOf0 ) )
                & ! [B: $i] :
                    ( ( A @ ( B @ aElementOf0 ) )
                   => ( xS @ ( B @ aElementOf0 ) ) )
                & ( A @ aSet0 ) ) ) )
       => ( ( ( xk @ ( xS @ slbdtsldtrb0 ) )
            = slcrc0 )
          | ~ ? [A: $i] : ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ ( xk @ ( xS @ slbdtsldtrb0 ) @ aSubsetOf0 ) )
    & ! [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
       => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
    & ! [A: $i] :
        ( ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( ( xT @ ( A @ aSubsetOf0 ) )
            | ( ! [B: $i] :
                  ( ( A @ ( B @ aElementOf0 ) )
                 => ( xT @ ( B @ aElementOf0 ) ) )
              & ( A @ aSet0 ) ) ) )
       => ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
    & ! [A: $i] :
        ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
       => ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( xT @ ( A @ aSubsetOf0 ) )
          & ! [B: $i] :
              ( ( A @ ( B @ aElementOf0 ) )
             => ( xT @ ( B @ aElementOf0 ) ) )
          & ( A @ aSet0 ) ) )
    & ( xk @ ( xT @ slbdtsldtrb0 ) @ aSet0 )
    & ! [A: $i] :
        ( ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( ( xS @ ( A @ aSubsetOf0 ) )
            | ( ! [B: $i] :
                  ( ( A @ ( B @ aElementOf0 ) )
                 => ( xS @ ( B @ aElementOf0 ) ) )
              & ( A @ aSet0 ) ) ) )
       => ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
    & ! [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
       => ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( xS @ ( A @ aSubsetOf0 ) )
          & ! [B: $i] :
              ( ( A @ ( B @ aElementOf0 ) )
             => ( xS @ ( B @ aElementOf0 ) ) )
          & ( A @ aSet0 ) ) )
    & ( xk @ ( xS @ slbdtsldtrb0 ) @ aSet0 ) ),
    inference(miniscope,[status(thm)],[341]) ).

thf(343,plain,
    ! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( xk @ ( xS @ slbdtsldtrb0 ) )
       != slcrc0 )
      & ( xk @ ( xS @ slbdtsldtrb0 ) @ ( sk21 @ aElementOf0 ) )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( J @ aElementOf0 ) )
        | ( ( J @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( J @ aSubsetOf0 ) ) )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( J @ aElementOf0 ) )
        | ( ( J @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( J @ sk20 @ aElementOf0 ) )
        | ~ ( J @ aSet0 ) )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( J @ aElementOf0 ) )
        | ( ( J @ sbrdtbr0 )
         != xk )
        | ( J @ ( J @ sk20 @ aElementOf0 ) )
        | ~ ( J @ aSet0 ) )
      & ( ( ( H @ sbrdtbr0 )
          = xk )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( H @ aElementOf0 ) ) )
      & ( ( xS @ ( H @ aSubsetOf0 ) )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( H @ aElementOf0 ) ) )
      & ( ( xS @ ( I @ aElementOf0 ) )
        | ~ ( H @ ( I @ aElementOf0 ) )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( H @ aElementOf0 ) ) )
      & ( ( H @ aSet0 )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( H @ aElementOf0 ) ) )
      & ( xk @ ( xT @ slbdtsldtrb0 ) @ ( xk @ ( xS @ slbdtsldtrb0 ) @ aSubsetOf0 ) )
      & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( G @ aElementOf0 ) )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( G @ aElementOf0 ) ) )
      & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( F @ aElementOf0 ) )
        | ( ( F @ sbrdtbr0 )
         != xk )
        | ~ ( xT @ ( F @ aSubsetOf0 ) ) )
      & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( F @ aElementOf0 ) )
        | ( ( F @ sbrdtbr0 )
         != xk )
        | ~ ( xT @ ( F @ sk19 @ aElementOf0 ) )
        | ~ ( F @ aSet0 ) )
      & ( ( xk @ ( xT @ slbdtsldtrb0 ) @ ( F @ aElementOf0 ) )
        | ( ( F @ sbrdtbr0 )
         != xk )
        | ( F @ ( F @ sk19 @ aElementOf0 ) )
        | ~ ( F @ aSet0 ) )
      & ( ( ( D @ sbrdtbr0 )
          = xk )
        | ~ ( xk @ ( xT @ slbdtsldtrb0 ) @ ( D @ aElementOf0 ) ) )
      & ( ( xT @ ( D @ aSubsetOf0 ) )
        | ~ ( xk @ ( xT @ slbdtsldtrb0 ) @ ( D @ aElementOf0 ) ) )
      & ( ( xT @ ( E @ aElementOf0 ) )
        | ~ ( D @ ( E @ aElementOf0 ) )
        | ~ ( xk @ ( xT @ slbdtsldtrb0 ) @ ( D @ aElementOf0 ) ) )
      & ( ( D @ aSet0 )
        | ~ ( xk @ ( xT @ slbdtsldtrb0 ) @ ( D @ aElementOf0 ) ) )
      & ( xk @ ( xT @ slbdtsldtrb0 ) @ aSet0 )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( C @ aElementOf0 ) )
        | ( ( C @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( C @ aSubsetOf0 ) ) )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( C @ aElementOf0 ) )
        | ( ( C @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( C @ sk18 @ aElementOf0 ) )
        | ~ ( C @ aSet0 ) )
      & ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( C @ aElementOf0 ) )
        | ( ( C @ sbrdtbr0 )
         != xk )
        | ( C @ ( C @ sk18 @ aElementOf0 ) )
        | ~ ( C @ aSet0 ) )
      & ( ( ( A @ sbrdtbr0 )
          = xk )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
      & ( ( xS @ ( A @ aSubsetOf0 ) )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
      & ( ( xS @ ( B @ aElementOf0 ) )
        | ~ ( A @ ( B @ aElementOf0 ) )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
      & ( ( A @ aSet0 )
        | ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ) )
      & ( xk @ ( xS @ slbdtsldtrb0 ) @ aSet0 ) ),
    inference(cnf,[status(esa)],[342]) ).

thf(352,plain,
    xk @ ( xS @ slbdtsldtrb0 ) @ ( sk21 @ aElementOf0 ),
    inference(cnfConj,[status(thm)],[343]) ).

thf(1,conjecture,
    ? [A: $i] :
      ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
      | ( ( ( A @ sbrdtbr0 )
          = xk )
        & ( ( xS @ ( A @ aSubsetOf0 ) )
          | ( ! [B: $i] :
                ( ( A @ ( B @ aElementOf0 ) )
               => ( xS @ ( B @ aElementOf0 ) ) )
            & ( A @ aSet0 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ? [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
        | ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( ( xS @ ( A @ aSubsetOf0 ) )
            | ( ! [B: $i] :
                  ( ( A @ ( B @ aElementOf0 ) )
                 => ( xS @ ( B @ aElementOf0 ) ) )
              & ( A @ aSet0 ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(67,plain,
    ~ ? [A: $i] :
        ( ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
        | ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( ( xS @ ( A @ aSubsetOf0 ) )
            | ( ! [B: $i] :
                  ( ( A @ ( B @ aElementOf0 ) )
                 => ( xS @ ( B @ aElementOf0 ) ) )
              & ( A @ aSet0 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(68,plain,
    ~ ( ? [A: $i] : ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) )
      | ? [A: $i] :
          ( ( ( A @ sbrdtbr0 )
            = xk )
          & ( ( xS @ ( A @ aSubsetOf0 ) )
            | ( ! [B: $i] :
                  ( ( A @ ( B @ aElementOf0 ) )
                 => ( xS @ ( B @ aElementOf0 ) ) )
              & ( A @ aSet0 ) ) ) ) ),
    inference(miniscope,[status(thm)],[67]) ).

thf(69,plain,
    ! [B: $i,A: $i] :
      ( ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( B @ aElementOf0 ) )
      & ( ( ( A @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( A @ aSubsetOf0 ) ) )
      & ( ( ( A @ sbrdtbr0 )
         != xk )
        | ~ ( xS @ ( A @ sk1 @ aElementOf0 ) )
        | ~ ( A @ aSet0 ) )
      & ( ( ( A @ sbrdtbr0 )
         != xk )
        | ( A @ ( A @ sk1 @ aElementOf0 ) )
        | ~ ( A @ aSet0 ) ) ),
    inference(cnf,[status(esa)],[68]) ).

thf(73,plain,
    ! [A: $i] :
      ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ),
    inference(cnfConj,[status(thm)],[69]) ).

thf(77,plain,
    ! [A: $i] :
      ~ ( xk @ ( xS @ slbdtsldtrb0 ) @ ( A @ aElementOf0 ) ),
    inference(simp,[status(thm)],[73]) ).

thf(548,plain,
    $false,
    inference(rewrite,[status(thm)],[352,77]) ).

thf(549,plain,
    $false,
    inference(simp,[status(thm)],[548]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM547+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39  % Computer : n014.cluster.edu
% 0.12/0.39  % Model    : x86_64 x86_64
% 0.12/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39  % Memory   : 8046.5625MB
% 0.12/0.39  % OS       : Linux 6.8.0-71-generic
% 0.12/0.39  % CPULimit : 300
% 0.12/0.39  % WCLimit  : 300
% 0.12/0.39  % DateTime : Sat Sep 26 03:10:46 UTC 2026
% 0.12/0.40  % CPUTime  : 
% 0.12/0.40  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.44/1.23  % [INFO] 	 Parsing done (252ms). 
% 1.44/1.24  % [INFO] 	 Running in sequential loop mode. 
% 2.30/1.65  % [INFO] 	 eprover registered as external prover. 
% 2.30/1.66  % [INFO] 	 Scanning for conjecture ... 
% 2.52/1.72  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.73  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.75  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.75  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.77  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.77  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.78  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.52/1.79  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.76/1.82  % [INFO] 	 Found a conjecture (or negated_conjecture) and 64 axioms. Running axiom selection ... 
% 2.98/1.92  % [INFO] 	 Axiom selection finished. Selected 64 axioms (removed 0 axioms). 
% 2.98/1.93  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.95  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.96  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.96  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.97  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.97  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/1.98  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/2.00  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.98/2.00  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.98/2.02  % [INFO] 	 Type checking passed. 
% 2.98/2.02  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 8.75/3.84  % [INFO] 	 Killing All external provers ... 
% 8.75/3.85  % Time passed: 3302ms (effective reasoning time: 2596ms)
% 8.75/3.85  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.75/3.85  % Axioms used in derivation (1): m__2227
% 8.75/3.85  % No. of inferences in proof: 14
% 8.75/3.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3302 ms resp. 2596 ms w/o parsing
% 9.17/3.91  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.17/3.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------