TSTP Solution File: LCL947_10 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n022.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 00:08:47 EDT 2024

% Result   : Theorem 6.64s 2.77s
% Output   : Refutation 7.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   50 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :  453 (   0 equ;   0 cnn)
%            Maximal formula atoms :   34 (  10 avg)
%            Number of connectives : 1470 (   2   ~;   4   |;  28   &;1057   @)
%                                         (   0 <=>; 379  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   26 (  17 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :  343 (   0   ^ 341   !;   2   ?; 343   :)

% 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(qmltpeq_type,type,
    qmltpeq: '\'$ki_world\'' > $i > $i > $o ).

thf(member_type,type,
    member: '\'$ki_world\'' > $i > $i > $o ).

thf(subset_type,type,
    subset: '\'$ki_world\'' > $i > $i > $o ).

thf(union_type,type,
    union: $i > $i > $i ).

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

thf(12,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( subset @ H @ B @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( subset @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_1) ).

thf(101,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( subset @ H @ B @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( subset @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(13,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ B @ D ) )
                       => ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ D @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).

thf(106,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ B @ D ) )
                       => ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ D @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(20,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( subset @ F @ B @ D ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ F @ H )
                                     => ( ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ B ) )
                                       => ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ D ) ) ) ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ F @ H )
                                     => ( ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ B ) )
                                       => ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ D ) ) ) ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( subset @ F @ B @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

thf(129,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( subset @ F @ B @ D ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ F @ H )
                                     => ( ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ B ) )
                                       => ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ D ) ) ) ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ F @ H )
                                     => ( ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ B ) )
                                       => ! [I: '\'$ki_world\''] :
                                            ( ( '\'$ki_accessible\'' @ H @ I )
                                           => ( member @ I @ G @ D ) ) ) ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( subset @ F @ B @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(9,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( qmltpeq @ E @ ( union @ B @ D ) @ ( union @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

thf(91,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( qmltpeq @ E @ ( union @ B @ D ) @ ( union @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(16,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ B ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( member @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_2) ).

thf(114,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ B ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( member @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(17,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ D ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ ( union @ F @ B ) @ ( union @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_2) ).

thf(119,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ D ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ ( union @ F @ B ) @ ( union @ F @ D ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(21,axiom,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

thf(146,plain,
    ! [A: '\'$ki_world\''] : ( '\'$ki_accessible\'' @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(7,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) ) ) )
                                    & ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) ) ) ) ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) ) ) )
                                    & ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) ) ) ) ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

thf(47,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) ) ) )
                                    & ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) ) ) ) ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ! [G: $i] :
                                  ( ( '\'$ki_exists_in_world_$i\'' @ F @ G )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) ) ) )
                                    & ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ F @ H )
                                       => ( ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ D ) )
                                         => ! [I: '\'$ki_world\''] :
                                              ( ( '\'$ki_accessible\'' @ H @ I )
                                             => ( member @ I @ G @ B ) ) ) ) ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(10,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ B @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( member @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_substitution_1) ).

thf(93,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ B @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( member @ H @ D @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(4,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ D @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ F ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

thf(29,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ D @ F ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ F ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(14,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 )
             => ( qmltpeq @ C @ B @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

thf(109,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 )
             => ( qmltpeq @ C @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(19,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( subset @ H @ F @ B ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( subset @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_substitution_2) ).

thf(124,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( qmltpeq @ H @ B @ D ) )
                                  & ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( subset @ H @ F @ B ) ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( subset @ H @ F @ D ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(5,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ( ! [G: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ G )
                               => ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ ( union @ B @ D ) ) )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ B ) )
                                    | ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ D ) ) ) ) )
                            & ! [G: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ G )
                               => ( ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ B ) )
                                    | ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ D ) ) )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ ( union @ B @ D ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

thf(34,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ( ! [G: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ G )
                               => ( ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ ( union @ B @ D ) ) )
                                 => ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ B ) )
                                    | ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ D ) ) ) ) )
                            & ! [G: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ G )
                               => ( ( ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ B ) )
                                    | ! [H: '\'$ki_world\''] :
                                        ( ( '\'$ki_accessible\'' @ G @ H )
                                       => ( member @ H @ F @ D ) ) )
                                 => ! [H: '\'$ki_world\''] :
                                      ( ( '\'$ki_accessible\'' @ G @ H )
                                     => ( member @ H @ F @ ( union @ B @ D ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(6,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_nonempty') ).

thf(45,plain,
    ! [A: '\'$ki_world\''] :
    ? [B: $i] : ( '\'$ki_exists_in_world_$i\'' @ A @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1,conjecture,
    ! [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 )
             => ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
    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_$i\'' @ A @ B )
           => ! [C: '\'$ki_world\''] :
                ( ( '\'$ki_accessible\'' @ A @ C )
               => ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(22,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 )
               => ( qmltpeq @ C @ ( union @ B @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

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

thf(27,plain,
    ! [A: '\'$ki_world\'',B: '\'$ki_world\'',C: '\'$ki_world\''] :
      ( ( ( '\'$ki_accessible\'' @ A @ B )
        & ( '\'$ki_accessible\'' @ B @ C ) )
     => ( '\'$ki_accessible\'' @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(8,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) )
                         => ( ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ B @ D ) )
                            & ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ D @ B ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ( ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ B @ D ) )
                            & ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ D @ B ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

thf(76,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ( ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) )
                         => ( ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ B @ D ) )
                            & ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ D @ B ) ) ) ) )
                    & ! [E: '\'$ki_world\''] :
                        ( ( '\'$ki_accessible\'' @ C @ E )
                       => ( ( ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ B @ D ) )
                            & ! [F: '\'$ki_world\''] :
                                ( ( '\'$ki_accessible\'' @ E @ F )
                               => ( subset @ F @ D @ B ) ) )
                         => ! [F: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ F )
                             => ( qmltpeq @ F @ B @ D ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(11,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( subset @ F @ B @ D ) )
                       => ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ ( union @ B @ D ) @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).

thf(98,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ( ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( subset @ F @ B @ D ) )
                       => ! [F: '\'$ki_world\''] :
                            ( ( '\'$ki_accessible\'' @ E @ F )
                           => ( qmltpeq @ F @ ( union @ B @ D ) @ D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(15,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ D ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ ( union @ B @ F ) @ ( union @ D @ F ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_substitution_1) ).

thf(111,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 )
             => ! [D: $i] :
                  ( ( '\'$ki_exists_in_world_$i\'' @ C @ D )
                 => ! [E: '\'$ki_world\''] :
                      ( ( '\'$ki_accessible\'' @ C @ E )
                     => ! [F: $i] :
                          ( ( '\'$ki_exists_in_world_$i\'' @ E @ F )
                         => ! [G: '\'$ki_world\''] :
                              ( ( '\'$ki_accessible\'' @ E @ G )
                             => ( ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ B @ D ) )
                               => ! [H: '\'$ki_world\''] :
                                    ( ( '\'$ki_accessible\'' @ G @ H )
                                   => ( qmltpeq @ H @ ( union @ B @ F ) @ ( union @ D @ F ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(18,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 )
             => ( subset @ C @ B @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).

thf(122,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 )
             => ( subset @ C @ B @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(209,plain,
    $false,
    inference(e,[status(thm)],[101,106,129,91,114,119,146,47,93,29,109,124,34,45,22,27,76,98,111,122]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14  % Problem  : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% 0.11/0.17  % Command  : run_Leo-III %s %d
% 0.15/0.38  % Computer : n022.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Mon May 20 01:50:09 EDT 2024
% 0.15/0.38  % CPUTime  : 
% 0.96/0.92  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.49/1.08  % [INFO] 	 Parsing done (162ms). 
% 1.49/1.09  % [INFO] 	 Running in sequential loop mode. 
% 1.92/1.33  % [INFO] 	 eprover registered as external prover. 
% 1.92/1.33  % [INFO] 	 cvc4 registered as external prover. 
% 1.92/1.34  % [INFO] 	 Scanning for conjecture ... 
% 2.11/1.41  % [INFO] 	 Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ... 
% 2.38/1.47  % [INFO] 	 Axiom selection finished. Selected 19 axioms (removed 0 axioms). 
% 2.62/1.57  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 2.62/1.59  % [INFO] 	 Type checking passed. 
% 2.62/1.59  % [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 ... 
% 6.64/2.76  % External prover 'e' found a proof!
% 6.64/2.76  % [INFO] 	 Killing All external provers ... 
% 6.64/2.76  % Time passed: 2230ms (effective reasoning time: 1669ms)
% 6.64/2.76  % 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)>
% 6.64/2.77  % Axioms used in derivation (19): member_substitution_1, equal_member_defn, union_substitution_2, subset_union, member_substitution_2, symmetry, reflexivity_of_subset, $ki_exists_in_world_$i_nonempty, mrel_reflexive, subset_substitution_2, reflexivity, commutativity_of_union, subset_substitution_1, union_substitution_1, mrel_transitive, equal_defn, transitivity, union_defn, subset_defn
% 6.64/2.77  % No. of inferences in proof: 42
% 6.64/2.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2230 ms resp. 1669 ms w/o parsing
% 7.01/2.82  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.01/2.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------