TPTP Problem File: LCL945_9.p

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%------------------------------------------------------------------------------
% File     : LCL945_9 : TPTP v8.2.0. Released v8.2.0.
% Domain   : Natural Language Processing
% Problem  : Goedel translation of NLP001+1
% Version  : [QMLTP] axioms.
% English  : 

% Refs     : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
% Source   : [QMLTP]
% Names    : GNL001+1 [QMLTP]

% Status   : Theorem
% Rating   : 1.00 v8.2.0
% Syntax   : Number of formulae    :   21 (   2 unt;  18 typ;   0 def)
%            Number of atoms       :  132 (   0 equ)
%            Maximal formula atoms :  130 (  44 avg)
%            Number of connectives :  129 (   0   ~;   0   |;  69   &)
%                                         (   0 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (  11 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   35 (  16   >;  19   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  16 usr;   0 prp; 2-3 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   78 (;  60   !;  18   ?;  78   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_D, TFF embedding.
%------------------------------------------------------------------------------
tff('$ki_world_type',type,
    '$ki_world': $tType ).

tff('$ki_local_world_decl',type,
    '$ki_local_world': '$ki_world' ).

tff('$ki_accessible_decl',type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(mrel_serial,axiom,
    ! [W: '$ki_world'] :
    ? [V: '$ki_world'] : '$ki_accessible'(W,V) ).

tff(chevy_decl,type,
    chevy: ( '$ki_world' * $i ) > $o ).

tff(dirty_decl,type,
    dirty: ( '$ki_world' * $i ) > $o ).

tff(barrel_decl,type,
    barrel: ( '$ki_world' * $i * $i ) > $o ).

tff(hollywood_decl,type,
    hollywood: ( '$ki_world' * $i ) > $o ).

tff(city_decl,type,
    city: ( '$ki_world' * $i ) > $o ).

tff(in_decl,type,
    in: ( '$ki_world' * $i * $i ) > $o ).

tff(old_decl,type,
    old: ( '$ki_world' * $i ) > $o ).

tff(down_decl,type,
    down: ( '$ki_world' * $i * $i ) > $o ).

tff(way_decl,type,
    way: ( '$ki_world' * $i ) > $o ).

tff(white_decl,type,
    white: ( '$ki_world' * $i ) > $o ).

tff(car_decl,type,
    car: ( '$ki_world' * $i ) > $o ).

tff(street_decl,type,
    street: ( '$ki_world' * $i ) > $o ).

tff(event_decl,type,
    event: ( '$ki_world' * $i ) > $o ).

tff(lonely_decl,type,
    lonely: ( '$ki_world' * $i ) > $o ).

tff('$ki_exists_in_world_$i_decl',type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff('$ki_exists_in_world_$i_nonempty',axiom,
    ! [W: '$ki_world'] :
    ? [X: $i] : '$ki_exists_in_world_$i'(W,X) ).

tff(verify,conjecture,
    ( ! [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
       => ( ? [U: $i] :
              ( '$ki_exists_in_world_$i'(W,U)
              & ? [V: $i] :
                  ( '$ki_exists_in_world_$i'(W,V)
                  & ? [W: $i] :
                      ( '$ki_exists_in_world_$i'(W,W)
                      & ? [X: $i] :
                          ( '$ki_exists_in_world_$i'(W,X)
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => hollywood(W0,U) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => city(W0,U) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => event(W0,V) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => street(W0,W) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => way(W0,W) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => lonely(W0,W) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => chevy(W0,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => car(W0,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => white(W0,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => dirty(W0,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => old(W0,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => barrel(W0,V,X) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => down(W0,V,W) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => in(W0,V,U) ) ) ) ) )
         => ? [Y: $i] :
              ( '$ki_exists_in_world_$i'(W,Y)
              & ? [Z: $i] :
                  ( '$ki_exists_in_world_$i'(W,Z)
                  & ? [X1: $i] :
                      ( '$ki_exists_in_world_$i'(W,X1)
                      & ? [X2: $i] :
                          ( '$ki_exists_in_world_$i'(W,X2)
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => hollywood(W0,Y) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => city(W0,Y) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => event(W0,Z) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => chevy(W0,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => car(W0,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => white(W0,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => dirty(W0,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => old(W0,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => street(W0,X2) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => way(W0,X2) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => lonely(W0,X2) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => barrel(W0,Z,X1) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => down(W0,Z,X2) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => in(W0,Z,Y) ) ) ) ) ) ) )
    & ! [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
       => ( ? [X3: $i] :
              ( '$ki_exists_in_world_$i'(W,X3)
              & ? [X4: $i] :
                  ( '$ki_exists_in_world_$i'(W,X4)
                  & ? [X5: $i] :
                      ( '$ki_exists_in_world_$i'(W,X5)
                      & ? [X6: $i] :
                          ( '$ki_exists_in_world_$i'(W,X6)
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => hollywood(W0,X3) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => city(W0,X3) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => event(W0,X4) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => chevy(W0,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => car(W0,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => white(W0,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => dirty(W0,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => old(W0,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => street(W0,X6) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => way(W0,X6) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => lonely(W0,X6) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => barrel(W0,X4,X5) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => down(W0,X4,X6) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => in(W0,X4,X3) ) ) ) ) )
         => ? [X7: $i] :
              ( '$ki_exists_in_world_$i'(W,X7)
              & ? [X8: $i] :
                  ( '$ki_exists_in_world_$i'(W,X8)
                  & ? [X9: $i] :
                      ( '$ki_exists_in_world_$i'(W,X9)
                      & ? [X10: $i] :
                          ( '$ki_exists_in_world_$i'(W,X10)
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => hollywood(W0,X7) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => city(W0,X7) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => event(W0,X8) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => street(W0,X9) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => way(W0,X9) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => lonely(W0,X9) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => chevy(W0,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => car(W0,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => white(W0,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => dirty(W0,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => old(W0,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => barrel(W0,X8,X10) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => down(W0,X8,X9) )
                          & ! [W0: '$ki_world'] :
                              ( '$ki_accessible'(W,W0)
                             => in(W0,X8,X7) ) ) ) ) ) ) ) ) ).

%------------------------------------------------------------------------------