TPTP Problem File: LCL945_9.p

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%------------------------------------------------------------------------------
% File     : LCL945_9 : TPTP v9.0.0. Bugfixed v9.0.0.
% 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   : 0.33 v9.0.0
% Syntax   : Number of formulae    :   19 (   1 unt;  17 typ;   0 def)
%            Number of atoms       :  115 (   0 equ)
%            Maximal formula atoms :  114 (  57 avg)
%            Number of connectives :  113 (   0   ~;   0   |;  53   &)
%                                         (   0 <=>;  60  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (  14 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   33 (  15   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  15 usr;   0 prp; 2-3 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   77 (  60   !;  17   ?;  77   :)
% SPC      : TF0_THM_NEQ_NAR

% Comments : Generated by embedproblem, version 1.7.14, rigid constant, 
%            modal_system_D, TFF embedding.
% Bugfixes : v9.0.0 - Fixed embedding variables
%------------------------------------------------------------------------------
%----Meta-logical definitions of the embedding
tff('$world_type',type,
    '$world': $tType ).

tff('$local_world_decl',type,
    '$local_world': '$world' ).

tff('$accessible_world_decl',type,
    '$accessible_world': ( '$world' * '$world' ) > $o ).

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

%----Converted user type declarations 
tff(chevy_type,type,
    chevy: ( '$world' * $i ) > $o ).

tff(dirty_type,type,
    dirty: ( '$world' * $i ) > $o ).

tff(barrel_type,type,
    barrel: ( '$world' * $i * $i ) > $o ).

tff(hollywood_type,type,
    hollywood: ( '$world' * $i ) > $o ).

tff(city_type,type,
    city: ( '$world' * $i ) > $o ).

tff(in_type,type,
    in: ( '$world' * $i * $i ) > $o ).

tff(old_type,type,
    old: ( '$world' * $i ) > $o ).

tff(down_type,type,
    down: ( '$world' * $i * $i ) > $o ).

tff(way_type,type,
    way: ( '$world' * $i ) > $o ).

tff(white_type,type,
    white: ( '$world' * $i ) > $o ).

tff(car_type,type,
    car: ( '$world' * $i ) > $o ).

tff(street_type,type,
    street: ( '$world' * $i ) > $o ).

tff(event_type,type,
    event: ( '$world' * $i ) > $o ).

tff(lonely_type,type,
    lonely: ( '$world' * $i ) > $o ).

tff(co1,conjecture,
    ! [W: '$world'] :
      ( ! [W0: '$world'] :
          ( '$accessible_world'(W,W0)
         => ( ? [U: $i,V: $i,WW: $i,X: $i] :
                ( ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => hollywood(W1,U) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => city(W1,U) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => event(W1,V) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => street(W1,WW) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => way(W1,WW) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => lonely(W1,WW) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => chevy(W1,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => car(W1,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => white(W1,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => dirty(W1,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => old(W1,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => barrel(W1,V,X) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => down(W1,V,WW) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => in(W1,V,U) ) )
           => ? [Y: $i,Z: $i,X1: $i,X2: $i] :
                ( ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => hollywood(W1,Y) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => city(W1,Y) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => event(W1,Z) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => chevy(W1,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => car(W1,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => white(W1,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => dirty(W1,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => old(W1,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => street(W1,X2) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => way(W1,X2) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => lonely(W1,X2) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => barrel(W1,Z,X1) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => down(W1,Z,X2) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => in(W1,Z,Y) ) ) ) )
      & ! [W0: '$world'] :
          ( '$accessible_world'(W,W0)
         => ( ? [X3: $i,X4: $i,X5: $i,X6: $i] :
                ( ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => hollywood(W1,X3) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => city(W1,X3) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => event(W1,X4) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => chevy(W1,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => car(W1,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => white(W1,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => dirty(W1,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => old(W1,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => street(W1,X6) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => way(W1,X6) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => lonely(W1,X6) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => barrel(W1,X4,X5) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => down(W1,X4,X6) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => in(W1,X4,X3) ) )
           => ? [X7: $i,X8: $i,X9: $i,X10: $i] :
                ( ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => hollywood(W1,X7) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => city(W1,X7) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => event(W1,X8) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => street(W1,X9) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => way(W1,X9) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => lonely(W1,X9) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => chevy(W1,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => car(W1,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => white(W1,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => dirty(W1,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => old(W1,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => barrel(W1,X8,X10) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => down(W1,X8,X9) )
                & ! [W1: '$world'] :
                    ( '$accessible_world'(W0,W1)
                   => in(W1,X8,X7) ) ) ) ) ) ).

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