TSTP Solution File: NUM588+3 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NUM588+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.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 : Tue May 21 01:35:19 EDT 2024

% Result   : Theorem 15.70s 4.38s
% Output   : Refutation 15.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   34 (   6 unt;  18 typ;   0 def)
%            Number of atoms       :  166 (  18 equ;   0 cnn)
%            Maximal formula atoms :   40 (  10 avg)
%            Number of connectives :  906 (  25   ~;  14   |;  80   &; 735   @)
%                                         (   4 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  17   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  18 usr;   9 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

% Comments : 
%------------------------------------------------------------------------------
thf(aSet0_type,type,
    aSet0: $i > $o ).

thf(aElementOf0_type,type,
    aElementOf0: $i > $i > $o ).

thf(aSubsetOf0_type,type,
    aSubsetOf0: $i > $i > $o ).

thf(aElement0_type,type,
    aElement0: $i > $o ).

thf(sdtmndt0_type,type,
    sdtmndt0: $i > $i > $i ).

thf(szNzAzT0_type,type,
    szNzAzT0: $i ).

thf(szmzizndt0_type,type,
    szmzizndt0: $i > $i ).

thf(sdtlseqdt0_type,type,
    sdtlseqdt0: $i > $i > $o ).

thf(slbdtsldtrb0_type,type,
    slbdtsldtrb0: $i > $i > $i ).

thf(sbrdtbr0_type,type,
    sbrdtbr0: $i > $i ).

thf(sdtlpdtrp0_type,type,
    sdtlpdtrp0: $i > $i > $i ).

thf(xN_type,type,
    xN: $i ).

thf(isCountable0_type,type,
    isCountable0: $i > $o ).

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

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ szNzAzT0 )
     => ! [B: $i] :
          ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
               => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
            & ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              <=> ( ( aElement0 @ C )
                  & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                  & ( C
                   != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
            & ( aSet0 @ B )
            & ! [C: $i] :
                ( ( aElementOf0 @ C @ B )
               => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
            & ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
            & ( isCountable0 @ B ) )
         => ! [C: $i] :
              ( ( ( aSet0 @ C )
                & ! [D: $i] :
                    ( ( aElementOf0 @ D @ C )
                   => ( aElementOf0 @ D @ B ) )
                & ( aSubsetOf0 @ C @ B )
                & ( ( sbrdtbr0 @ C )
                  = xk )
                & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
             => ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                     => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) ) )
               => ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                    & ! [D: $i] :
                        ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      <=> ( ( aElement0 @ D )
                          & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                          & ( D
                           != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
                 => ( ! [D: $i] :
                        ( ( aElementOf0 @ D @ C )
                       => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                    | ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                    | ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

thf(2,negated_conjecture,
    ~ ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ! [B: $i] :
            ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                 => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
              & ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                <=> ( ( aElement0 @ C )
                    & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ( C
                     != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ( isCountable0 @ B ) )
           => ! [C: $i] :
                ( ( ( aSet0 @ C )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ C )
                     => ( aElementOf0 @ D @ B ) )
                  & ( aSubsetOf0 @ C @ B )
                  & ( ( sbrdtbr0 @ C )
                    = xk )
                  & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
               => ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ! [D: $i] :
                        ( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                       => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) ) )
                 => ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      & ! [D: $i] :
                          ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                        <=> ( ( aElement0 @ D )
                            & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                            & ( D
                             != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
                   => ( ! [D: $i] :
                          ( ( aElementOf0 @ D @ C )
                         => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                      | ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      | ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(90,plain,
    ~ ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ! [B: $i] :
            ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                 => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
              & ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ! [C: $i] :
                  ( ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                   => ( ( aElement0 @ C )
                      & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                      & ( C
                       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                  & ( ( ( aElement0 @ C )
                      & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                      & ( C
                       != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                   => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
              & ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ( isCountable0 @ B ) )
           => ! [C: $i] :
                ( ( ( aSet0 @ C )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ C )
                     => ( aElementOf0 @ D @ B ) )
                  & ( aSubsetOf0 @ C @ B )
                  & ( ( sbrdtbr0 @ C )
                    = xk )
                  & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
               => ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ! [D: $i] :
                        ( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                       => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) ) )
                 => ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      & ! [D: $i] :
                          ( ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                           => ( ( aElement0 @ D )
                              & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                              & ( D
                               != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                          & ( ( ( aElement0 @ D )
                              & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                              & ( D
                               != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                           => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) ) )
                   => ( ! [D: $i] :
                          ( ( aElementOf0 @ D @ C )
                         => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                      | ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      | ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(91,plain,
    ~ ! [A: $i] :
        ( ( aElementOf0 @ A @ szNzAzT0 )
       => ! [B: $i] :
            ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                 => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ C ) )
              & ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                 => ( ( aElement0 @ C )
                    & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ( C
                     != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ! [C: $i] :
                  ( ( ( aElement0 @ C )
                    & ( aElementOf0 @ C @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ( C
                     != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                 => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ( aSet0 @ B )
              & ! [C: $i] :
                  ( ( aElementOf0 @ C @ B )
                 => ( aElementOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
              & ( aSubsetOf0 @ B @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
              & ( isCountable0 @ B ) )
           => ! [C: $i] :
                ( ( ( aSet0 @ C )
                  & ! [D: $i] :
                      ( ( aElementOf0 @ D @ C )
                     => ( aElementOf0 @ D @ B ) )
                  & ( aSubsetOf0 @ C @ B )
                  & ( ( sbrdtbr0 @ C )
                    = xk )
                  & ( aElementOf0 @ C @ ( slbdtsldtrb0 @ B @ xk ) ) )
               => ( ( ( aElementOf0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ ( sdtlpdtrp0 @ xN @ A ) )
                    & ! [D: $i] :
                        ( ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                       => ( sdtlseqdt0 @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) @ D ) ) )
                 => ( ( ( aSet0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      & ! [D: $i] :
                          ( ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                         => ( ( aElement0 @ D )
                            & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                            & ( D
                             != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                      & ! [D: $i] :
                          ( ( ( aElement0 @ D )
                            & ( aElementOf0 @ D @ ( sdtlpdtrp0 @ xN @ A ) )
                            & ( D
                             != ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                         => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) ) )
                   => ( ! [D: $i] :
                          ( ( aElementOf0 @ D @ C )
                         => ( aElementOf0 @ D @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) ) )
                      | ( aSubsetOf0 @ C @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) )
                      | ( aElementOf0 @ C @ ( slbdtsldtrb0 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ A ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ A ) ) ) @ xk ) ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[90]) ).

thf(115,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ sk2 )
      | ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) ) ) ) ),
    inference(cnf,[status(esa)],[91]) ).

thf(118,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ sk2 )
      | ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) ) ) ) ),
    inference(simp,[status(thm)],[115]) ).

thf(116,plain,
    ~ ( aElementOf0 @ sk4 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) ) ) ),
    inference(cnf,[status(esa)],[91]) ).

thf(1508,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ sk2 )
      | ( ( aElementOf0 @ A @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) ) ) )
       != ( aElementOf0 @ sk4 @ ( sdtmndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) @ ( szmzizndt0 @ ( sdtlpdtrp0 @ xN @ sk1 ) ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[118,116]) ).

thf(1509,plain,
    ~ ( aElementOf0 @ sk4 @ sk2 ),
    inference(pattern_uni,[status(thm)],[1508:[bind(A,$thf( sk4 ))]]) ).

thf(107,plain,
    aElementOf0 @ sk4 @ sk3,
    inference(cnf,[status(esa)],[91]) ).

thf(112,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ sk3 )
      | ( aElementOf0 @ A @ sk2 ) ),
    inference(cnf,[status(esa)],[91]) ).

thf(122,plain,
    ! [A: $i] :
      ( ~ ( aElementOf0 @ A @ sk3 )
      | ( aElementOf0 @ A @ sk2 ) ),
    inference(simp,[status(thm)],[112]) ).

thf(949,plain,
    ! [A: $i] :
      ( ( aElementOf0 @ A @ sk2 )
      | ( ( aElementOf0 @ sk4 @ sk3 )
       != ( aElementOf0 @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[107,122]) ).

thf(950,plain,
    aElementOf0 @ sk4 @ sk2,
    inference(pattern_uni,[status(thm)],[949:[bind(A,$thf( sk4 ))]]) ).

thf(1585,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[1509,950]) ).

thf(1586,plain,
    $false,
    inference(simp,[status(thm)],[1585]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : NUM588+3 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.38  % Computer : n021.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit : 300
% 0.16/0.38  % WCLimit  : 300
% 0.16/0.38  % DateTime : Mon May 20 06:00:24 EDT 2024
% 0.16/0.38  % CPUTime  : 
% 1.08/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.47/1.15  % [INFO] 	 Parsing done (200ms). 
% 1.47/1.16  % [INFO] 	 Running in sequential loop mode. 
% 2.33/1.40  % [INFO] 	 nitpick registered as external prover. 
% 2.33/1.41  % [INFO] 	 Scanning for conjecture ... 
% 2.33/1.46  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.51/1.47  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.53/1.48  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.53/1.48  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.53/1.49  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.53/1.50  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.53/1.50  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.64/1.51  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.64/1.52  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.64/1.52  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.64/1.53  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 2.70/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 87 axioms. Running axiom selection ... 
% 2.92/1.67  % [INFO] 	 Axiom selection finished. Selected 87 axioms (removed 0 axioms). 
% 2.92/1.68  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.71  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.71  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.71  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.72  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.72  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.72  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.73  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.74  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.74  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.74  % [INFO] 	 Definitions in FOF are currently treated as axioms. 
% 3.28/1.76  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 3.28/1.77  % [INFO] 	 Type checking passed. 
% 3.28/1.78  % [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 ... 
% 15.70/4.35  % [INFO] 	 Killing All external provers ... 
% 15.70/4.37  % Time passed: 3815ms (effective reasoning time: 3200ms)
% 15.70/4.38  % 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)>
% 15.70/4.38  % Axioms used in derivation (0): 
% 15.70/4.38  % No. of inferences in proof: 16
% 15.70/4.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3815 ms resp. 3200 ms w/o parsing
% 15.70/4.44  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.70/4.44  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------