%------------------------------------------------------------------------------
% File     : LCL970_15 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Goedel translation of SYN383+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    : GSY383+1 [QMLTP]

% Status   : CounterSatisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :   10 (   2 unt;   6 typ;   0 def)
%            Number of atoms       :   17 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :   13 (   0   ~;   1   |;   3   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   15 (;  12   !;   3   ?;  15   :)
% SPC      : TF0_CSA_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(big_q_decl,type,
    big_q: ( '$ki_world' * $i ) > $o ).

tff(big_p_decl,type,
    big_p: ( '$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_cumul',axiom,
    ! [W: '$ki_world',V: '$ki_world',X: $i] :
      ( ( '$ki_exists_in_world_$i'(W,X)
        & '$ki_accessible'(W,V) )
     => '$ki_exists_in_world_$i'(V,X) ) ).

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

tff(verify,conjecture,
    ? [X: $i] :
      ( '$ki_exists_in_world_$i'('$ki_local_world',X)
      & ! [W: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',W)
         => ! [Y: $i] :
              ( '$ki_exists_in_world_$i'(W,Y)
             => ! [W0: '$ki_world'] :
                  ( '$ki_accessible'(W,W0)
                 => ( ( ! [W1: '$ki_world'] :
                          ( '$ki_accessible'(W0,W1)
                         => big_p(W1,X) )
                      & ! [W1: '$ki_world'] :
                          ( '$ki_accessible'(W0,W1)
                         => big_q(W1,Y) ) )
                   => ( ! [W1: '$ki_world'] :
                          ( '$ki_accessible'(W0,W1)
                         => big_q(W1,X) )
                      | ! [W1: '$ki_world'] :
                          ( '$ki_accessible'(W0,W1)
                         => big_p(W1,Y) ) ) ) ) ) ) ) ).

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