TSTP Solution File: NLP266_23 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n025.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 01:00:35 EDT 2024

% Result   : Theorem 7.59s 3.28s
% Output   : Refutation 7.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   84 (  20 unt;  20 typ;   0 def)
%            Number of atoms       :  247 (   8 equ;   0 cnn)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 1195 ( 111   ~;  97   |;  33   &; 917   @)
%                                         (   0 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  13 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   43 (  43   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   22 (  19 usr;   7 con; 0-4 aty)
%            Number of variables   :  243 (   0   ^ 225   !;  18   ?; 243   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'$ki_world\'_type',type,
    '\'$ki_world\'': $tType ).

thf('\'$ki_local_world\'_type',type,
    '\'$ki_local_world\'': '\'$ki_world\'' ).

thf('\'$ki_accessible\'_type',type,
    '\'$ki_accessible\'': '\'$ki_world\'' > '\'$ki_world\'' > $o ).

thf(u_type,type,
    u: $i ).

thf(one_type,type,
    one: $i ).

thf(number_type,type,
    number: '\'$ki_world\'' > $i > $i > $o ).

thf(string_type,type,
    string: '\'$ki_world\'' > $i > $o ).

thf(in_type,type,
    in: '\'$ki_world\'' > $i > $i > $i > $o ).

thf(do_type,type,
    do: '\'$ki_world\'' > $i > $i > $i > $o ).

thf(entry_box_type,type,
    entry_box: '\'$ki_world\'' > $i > $o ).

thf(userid_type,type,
    userid: '\'$ki_world\'' > $i > $i > $o ).

thf('\'$ki_exists_in_world_$i\'_type',type,
    '\'$ki_exists_in_world_$i\'': '\'$ki_world\'' > $i > $o ).

thf(sk1_type,type,
    sk1: '\'$ki_world\'' ).

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

thf(sk3_type,type,
    sk3: $i > $i > $i > $i > '\'$ki_world\'' ).

thf(sk4_type,type,
    sk4: $i > $i > $i > $i > '\'$ki_world\'' ).

thf(sk5_type,type,
    sk5: $i > $i > $i > $i > $i ).

thf(sk7_type,type,
    sk7: '\'$ki_world\'' > $i ).

thf(sk8_type,type,
    sk8: $i ).

thf(sk9_type,type,
    sk9: $i > $i > $i > '\'$ki_world\'' > $i ).

thf(1,conjecture,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ? [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
              & ? [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                  & ? [E: $i] :
                      ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                      & ! [F: '\'$ki_world\''] :
                          ( ( '\'$ki_accessible\'' @ A @ F )
                         => ( ( userid @ F @ u @ B )
                            & ( entry_box @ F @ C )
                            & ( number @ F @ C @ one ) ) )
                      & ! [F: '\'$ki_world\''] :
                          ( ( '\'$ki_accessible\'' @ A @ F )
                         => ! [G: $i] :
                              ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                             => ( ( do @ F @ E @ D @ G )
                               => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

thf(2,negated_conjecture,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
       => ? [B: $i] :
            ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
            & ? [C: $i] :
                ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
                & ? [D: $i] :
                    ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                    & ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ( ( userid @ F @ u @ B )
                              & ( entry_box @ F @ C )
                              & ( number @ F @ C @ one ) ) )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ E @ D @ G )
                                 => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(9,plain,
    ~ ! [A: '\'$ki_world\''] :
        ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
       => ? [B: $i] :
            ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
            & ? [C: $i] :
                ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
                & ? [D: $i] :
                    ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                    & ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ( ( userid @ F @ u @ B )
                              & ( entry_box @ F @ C )
                              & ( number @ F @ C @ one ) ) )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ E @ D @ G )
                                 => ( in @ F @ B @ C @ G ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(13,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ B )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ C )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ D )
      | ( sk2 @ B @ A @ C @ D )
      | ( do @ ( sk4 @ D @ C @ B @ A ) @ D @ C @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(4,axiom,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

thf(19,plain,
    ! [A: '\'$ki_world\'',B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(20,plain,
    ! [B: $i,A: '\'$ki_world\''] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(cnf,[status(esa)],[19]) ).

thf(87,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ~ $true
      | ( sk2 @ B @ A @ C @ D )
      | ( do @ ( sk4 @ D @ C @ B @ A ) @ D @ C @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(rewrite,[status(thm)],[13,20]) ).

thf(88,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ B @ A @ C @ D )
      | ( do @ ( sk4 @ D @ C @ B @ A ) @ D @ C @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(simp,[status(thm)],[87]) ).

thf(6,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ! [C: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ A @ C )
             => ( ( userid @ C @ u @ B )
                & ( string @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

thf(23,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ? [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
          & ! [C: '\'$ki_world\''] :
              ( ( '\'$ki_accessible\'' @ A @ C )
             => ( ( userid @ C @ u @ B )
                & ( string @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(26,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ B )
      | ( userid @ B @ u @ ( sk7 @ A ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(3,axiom,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).

thf(17,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(18,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ B ),
    inference(cnf,[status(esa)],[17]) ).

thf(76,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ $true
      | ~ $true
      | ( userid @ B @ u @ ( sk7 @ A ) ) ),
    inference(rewrite,[status(thm)],[26,18]) ).

thf(77,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] : ( userid @ B @ u @ ( sk7 @ A ) ),
    inference(simp,[status(thm)],[76]) ).

thf(7,axiom,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ( ( entry_box @ B @ A )
            & ( number @ B @ A @ one ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

thf(27,plain,
    ? [A: $i] :
      ( ( '\'$ki_exists_in_world_$i\'' @ '\'$ki_local_world\'' @ A )
      & ! [B: '\'$ki_world\''] :
          ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ B )
         => ( ( entry_box @ B @ A )
            & ( number @ B @ A @ one ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(29,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ( number @ A @ sk8 @ one ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(57,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ $true
      | ( number @ A @ sk8 @ one ) ),
    inference(rewrite,[status(thm)],[29,18]) ).

thf(58,plain,
    ! [A: '\'$ki_world\''] : ( number @ A @ sk8 @ one ),
    inference(simp,[status(thm)],[57]) ).

thf(10,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ B )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ C )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ D )
      | ~ ( userid @ ( sk3 @ D @ C @ B @ A ) @ u @ A )
      | ~ ( entry_box @ ( sk3 @ D @ C @ B @ A ) @ B )
      | ~ ( number @ ( sk3 @ D @ C @ B @ A ) @ B @ one )
      | ~ ( sk2 @ B @ A @ C @ D ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(36,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ~ $true
      | ~ ( userid @ ( sk3 @ D @ C @ B @ A ) @ u @ A )
      | ~ ( entry_box @ ( sk3 @ D @ C @ B @ A ) @ B )
      | ~ ( number @ ( sk3 @ D @ C @ B @ A ) @ B @ one )
      | ~ ( sk2 @ B @ A @ C @ D ) ),
    inference(rewrite,[status(thm)],[10,20]) ).

thf(37,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( userid @ ( sk3 @ D @ C @ B @ A ) @ u @ A )
      | ~ ( entry_box @ ( sk3 @ D @ C @ B @ A ) @ B )
      | ~ ( number @ ( sk3 @ D @ C @ B @ A ) @ B @ one )
      | ~ ( sk2 @ B @ A @ C @ D ) ),
    inference(simp,[status(thm)],[36]) ).

thf(59,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ ( userid @ ( sk3 @ E @ D @ C @ B ) @ u @ B )
      | ~ ( entry_box @ ( sk3 @ E @ D @ C @ B ) @ C )
      | ~ ( sk2 @ C @ B @ D @ E )
      | ( ( number @ A @ sk8 @ one )
       != ( number @ ( sk3 @ E @ D @ C @ B ) @ C @ one ) ) ),
    inference(paramod_ordered,[status(thm)],[58,37]) ).

thf(60,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( userid @ ( sk3 @ A @ B @ sk8 @ C ) @ u @ C )
      | ~ ( entry_box @ ( sk3 @ A @ B @ sk8 @ C ) @ sk8 )
      | ~ ( sk2 @ sk8 @ C @ B @ A ) ),
    inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk3 @ F @ G @ sk8 @ I )),bind(B,$thf( I )),bind(C,$thf( sk8 )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).

thf(61,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( userid @ ( sk3 @ A @ B @ sk8 @ C ) @ u @ C )
      | ~ ( entry_box @ ( sk3 @ A @ B @ sk8 @ C ) @ sk8 )
      | ~ ( sk2 @ sk8 @ C @ B @ A ) ),
    inference(simp,[status(thm)],[60]) ).

thf(28,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ( entry_box @ A @ sk8 ) ),
    inference(cnf,[status(esa)],[27]) ).

thf(49,plain,
    ! [A: '\'$ki_world\''] :
      ( ~ $true
      | ( entry_box @ A @ sk8 ) ),
    inference(rewrite,[status(thm)],[28,18]) ).

thf(50,plain,
    ! [A: '\'$ki_world\''] : ( entry_box @ A @ sk8 ),
    inference(simp,[status(thm)],[49]) ).

thf(69,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( userid @ ( sk3 @ A @ B @ sk8 @ C ) @ u @ C )
      | ~ $true
      | ~ ( sk2 @ sk8 @ C @ B @ A ) ),
    inference(rewrite,[status(thm)],[61,50]) ).

thf(70,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( userid @ ( sk3 @ A @ B @ sk8 @ C ) @ u @ C )
      | ~ ( sk2 @ sk8 @ C @ B @ A ) ),
    inference(simp,[status(thm)],[69]) ).

thf(80,plain,
    ! [E: $i,D: $i,C: $i,B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( sk2 @ sk8 @ E @ D @ C )
      | ( ( userid @ B @ u @ ( sk7 @ A ) )
       != ( userid @ ( sk3 @ C @ D @ sk8 @ E ) @ u @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[77,70]) ).

thf(81,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] :
      ~ ( sk2 @ sk8 @ ( sk7 @ C ) @ B @ A ),
    inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( J )),bind(B,$thf( sk3 @ F @ G @ sk8 @ ( sk7 @ J ) )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( sk7 @ J ))]]) ).

thf(82,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] :
      ~ ( sk2 @ sk8 @ ( sk7 @ C ) @ B @ A ),
    inference(simp,[status(thm)],[81]) ).

thf(95,plain,
    ! [G: '\'$ki_world\'',F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( do @ ( sk4 @ D @ C @ B @ A ) @ D @ C @ ( sk5 @ D @ C @ B @ A ) )
      | ( ( sk2 @ B @ A @ C @ D )
       != ( sk2 @ sk8 @ ( sk7 @ G ) @ F @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[88,82]) ).

thf(96,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] : ( do @ ( sk4 @ B @ A @ sk8 @ ( sk7 @ C ) ) @ B @ A @ ( sk5 @ B @ A @ sk8 @ ( sk7 @ C ) ) ),
    inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk7 @ H )),bind(B,$thf( sk8 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( C )),bind(G,$thf( H ))]]) ).

thf(97,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] : ( do @ ( sk4 @ B @ A @ sk8 @ ( sk7 @ C ) ) @ B @ A @ ( sk5 @ B @ A @ sk8 @ ( sk7 @ C ) ) ),
    inference(simp,[status(thm)],[96]) ).

thf(25,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_accessible\'' @ A @ B )
      | ( string @ B @ ( sk7 @ A ) ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(64,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ $true
      | ~ $true
      | ( string @ B @ ( sk7 @ A ) ) ),
    inference(rewrite,[status(thm)],[25,18]) ).

thf(65,plain,
    ! [B: '\'$ki_world\'',A: '\'$ki_world\''] : ( string @ B @ ( sk7 @ A ) ),
    inference(simp,[status(thm)],[64]) ).

thf(8,axiom,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                 => ( ( ( string @ A @ C )
                      & ( entry_box @ A @ D ) )
                   => ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ B @ E @ G )
                                 => ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

thf(31,plain,
    ! [A: '\'$ki_world\''] :
      ( ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
     => ! [B: $i] :
          ( ( '\'$ki_exists_in_world_$i\'' @ A @ B )
         => ! [C: $i] :
              ( ( '\'$ki_exists_in_world_$i\'' @ A @ C )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ A @ D )
                 => ( ( ( string @ A @ C )
                      & ( entry_box @ A @ D ) )
                   => ? [E: $i] :
                        ( ( '\'$ki_exists_in_world_$i\'' @ A @ E )
                        & ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ A @ F )
                           => ! [G: $i] :
                                ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                               => ( ( do @ F @ B @ E @ G )
                                 => ( in @ F @ C @ D @ G ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(33,plain,
    ! [F: $i,E: '\'$ki_world\'',D: $i,C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ ( '\'$ki_accessible\'' @ '\'$ki_local_world\'' @ A )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ A @ B )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ A @ C )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ A @ D )
      | ~ ( string @ A @ C )
      | ~ ( entry_box @ A @ D )
      | ~ ( '\'$ki_accessible\'' @ A @ E )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ E @ F )
      | ~ ( do @ E @ B @ ( sk9 @ D @ C @ B @ A ) @ F )
      | ( in @ E @ C @ D @ F ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(38,plain,
    ! [F: $i,E: '\'$ki_world\'',D: $i,C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ~ $true
      | ~ ( string @ A @ C )
      | ~ ( entry_box @ A @ D )
      | ~ $true
      | ~ $true
      | ~ ( do @ E @ B @ ( sk9 @ D @ C @ B @ A ) @ F )
      | ( in @ E @ C @ D @ F ) ),
    inference(rewrite,[status(thm)],[33,18,20]) ).

thf(39,plain,
    ! [F: $i,E: '\'$ki_world\'',D: $i,C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ ( string @ A @ C )
      | ~ ( entry_box @ A @ D )
      | ~ ( do @ E @ B @ ( sk9 @ D @ C @ B @ A ) @ F )
      | ( in @ E @ C @ D @ F ) ),
    inference(simp,[status(thm)],[38]) ).

thf(53,plain,
    ! [G: $i,F: '\'$ki_world\'',E: $i,D: $i,C: $i,B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( string @ B @ D )
      | ~ ( do @ F @ C @ ( sk9 @ E @ D @ C @ B ) @ G )
      | ( in @ F @ D @ E @ G )
      | ( ( entry_box @ A @ sk8 )
       != ( entry_box @ B @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[50,39]) ).

thf(54,plain,
    ! [E: $i,D: '\'$ki_world\'',C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ ( string @ A @ C )
      | ~ ( do @ D @ B @ ( sk9 @ sk8 @ C @ B @ A ) @ E )
      | ( in @ D @ C @ sk8 @ E ) ),
    inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( sk8 ))]]) ).

thf(56,plain,
    ! [E: $i,D: '\'$ki_world\'',C: $i,B: $i,A: '\'$ki_world\''] :
      ( ~ ( string @ A @ C )
      | ~ ( do @ D @ B @ ( sk9 @ sk8 @ C @ B @ A ) @ E )
      | ( in @ D @ C @ sk8 @ E ) ),
    inference(simp,[status(thm)],[54]) ).

thf(138,plain,
    ! [G: $i,F: '\'$ki_world\'',E: $i,D: $i,C: '\'$ki_world\'',B: '\'$ki_world\'',A: '\'$ki_world\''] :
      ( ~ ( do @ F @ D @ ( sk9 @ sk8 @ E @ D @ C ) @ G )
      | ( in @ F @ E @ sk8 @ G )
      | ( ( string @ B @ ( sk7 @ A ) )
       != ( string @ C @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[65,56]) ).

thf(139,plain,
    ! [E: '\'$ki_world\'',D: $i,C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( do @ C @ B @ ( sk9 @ sk8 @ ( sk7 @ E ) @ B @ A ) @ D )
      | ( in @ C @ ( sk7 @ E ) @ sk8 @ D ) ),
    inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( sk7 @ H ))]]) ).

thf(148,plain,
    ! [E: '\'$ki_world\'',D: $i,C: '\'$ki_world\'',B: $i,A: '\'$ki_world\''] :
      ( ~ ( do @ C @ B @ ( sk9 @ sk8 @ ( sk7 @ E ) @ B @ A ) @ D )
      | ( in @ C @ ( sk7 @ E ) @ sk8 @ D ) ),
    inference(simp,[status(thm)],[139]) ).

thf(153,plain,
    ! [H: '\'$ki_world\'',G: $i,F: '\'$ki_world\'',E: $i,D: '\'$ki_world\'',C: '\'$ki_world\'',B: $i,A: $i] :
      ( ( in @ F @ ( sk7 @ H ) @ sk8 @ G )
      | ( ( do @ ( sk4 @ B @ A @ sk8 @ ( sk7 @ C ) ) @ B @ A @ ( sk5 @ B @ A @ sk8 @ ( sk7 @ C ) ) )
       != ( do @ F @ E @ ( sk9 @ sk8 @ ( sk7 @ H ) @ E @ D ) @ G ) ) ),
    inference(paramod_ordered,[status(thm)],[97,148]) ).

thf(154,plain,
    ! [D: '\'$ki_world\'',C: '\'$ki_world\'',B: '\'$ki_world\'',A: $i] : ( in @ ( sk4 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) @ ( sk7 @ C ) @ sk8 @ ( sk5 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) ),
    inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( sk9 @ sk8 @ ( sk7 @ ZA ) @ Y @ Z )),bind(B,$thf( Y )),bind(C,$thf( ZB )),bind(D,$thf( Z )),bind(E,$thf( Y )),bind(F,$thf( sk4 @ Y @ ( sk9 @ sk8 @ ( sk7 @ ZA ) @ Y @ Z ) @ sk8 @ ( sk7 @ ZB ) )),bind(G,$thf( sk5 @ Y @ ( sk9 @ sk8 @ ( sk7 @ ZA ) @ Y @ Z ) @ sk8 @ ( sk7 @ ZB ) )),bind(H,$thf( ZA ))]]) ).

thf(160,plain,
    ! [D: '\'$ki_world\'',C: '\'$ki_world\'',B: '\'$ki_world\'',A: $i] : ( in @ ( sk4 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) @ ( sk7 @ C ) @ sk8 @ ( sk5 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) ),
    inference(simp,[status(thm)],[154]) ).

thf(11,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ A )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ B )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ C )
      | ~ ( '\'$ki_exists_in_world_$i\'' @ sk1 @ D )
      | ( sk2 @ B @ A @ C @ D )
      | ~ ( in @ ( sk4 @ D @ C @ B @ A ) @ A @ B @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(45,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ $true
      | ~ $true
      | ~ $true
      | ( sk2 @ B @ A @ C @ D )
      | ~ ( in @ ( sk4 @ D @ C @ B @ A ) @ A @ B @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(rewrite,[status(thm)],[11,20]) ).

thf(46,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( sk2 @ B @ A @ C @ D )
      | ~ ( in @ ( sk4 @ D @ C @ B @ A ) @ A @ B @ ( sk5 @ D @ C @ B @ A ) ) ),
    inference(simp,[status(thm)],[45]) ).

thf(84,plain,
    ! [G: '\'$ki_world\'',F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( in @ ( sk4 @ D @ C @ B @ A ) @ A @ B @ ( sk5 @ D @ C @ B @ A ) )
      | ( ( sk2 @ B @ A @ C @ D )
       != ( sk2 @ sk8 @ ( sk7 @ G ) @ F @ E ) ) ),
    inference(paramod_ordered,[status(thm)],[46,82]) ).

thf(85,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] :
      ~ ( in @ ( sk4 @ B @ A @ sk8 @ ( sk7 @ C ) ) @ ( sk7 @ C ) @ sk8 @ ( sk5 @ B @ A @ sk8 @ ( sk7 @ C ) ) ),
    inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk7 @ H )),bind(B,$thf( sk8 )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( D )),bind(F,$thf( C )),bind(G,$thf( H ))]]) ).

thf(86,plain,
    ! [C: '\'$ki_world\'',B: $i,A: $i] :
      ~ ( in @ ( sk4 @ B @ A @ sk8 @ ( sk7 @ C ) ) @ ( sk7 @ C ) @ sk8 @ ( sk5 @ B @ A @ sk8 @ ( sk7 @ C ) ) ),
    inference(simp,[status(thm)],[85]) ).

thf(165,plain,
    ! [G: '\'$ki_world\'',F: $i,E: $i,D: '\'$ki_world\'',C: '\'$ki_world\'',B: '\'$ki_world\'',A: $i] :
      ( ( in @ ( sk4 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) @ ( sk7 @ C ) @ sk8 @ ( sk5 @ A @ ( sk9 @ sk8 @ ( sk7 @ C ) @ A @ B ) @ sk8 @ ( sk7 @ D ) ) )
     != ( in @ ( sk4 @ F @ E @ sk8 @ ( sk7 @ G ) ) @ ( sk7 @ G ) @ sk8 @ ( sk5 @ F @ E @ sk8 @ ( sk7 @ G ) ) ) ),
    inference(paramod_ordered,[status(thm)],[160,86]) ).

thf(166,plain,
    $false,
    inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( J )),bind(B,$thf( K )),bind(C,$thf( L )),bind(D,$thf( L )),bind(E,$thf( sk9 @ sk8 @ ( sk7 @ L ) @ J @ K )),bind(F,$thf( J )),bind(G,$thf( L ))]]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun May 19 22:12:09 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 1.08/1.01  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.39/1.24  % [INFO] 	 Parsing done (227ms). 
% 1.50/1.26  % [INFO] 	 Running in sequential loop mode. 
% 2.12/1.65  % [INFO] 	 nitpick registered as external prover. 
% 2.12/1.65  % [INFO] 	 Scanning for conjecture ... 
% 2.42/1.78  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 2.55/1.84  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 2.58/1.86  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.58/1.87  % [INFO] 	 Type checking passed. 
% 2.58/1.88  % [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 ... 
% 7.59/3.27  % [INFO] 	 Killing All external provers ... 
% 7.59/3.28  % Time passed: 2790ms (effective reasoning time: 2008ms)
% 7.59/3.28  % 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)>
% 7.59/3.28  % Axioms used in derivation (5): ax1, mrel_universal, ax2, $ki_exists_in_world_$i_const, ax3
% 7.59/3.28  % No. of inferences in proof: 64
% 7.59/3.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2790 ms resp. 2008 ms w/o parsing
% 7.66/3.40  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.66/3.40  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------