%------------------------------------------------------------------------------
% File     : LCL969_9 : TPTP v9.0.0. Released v8.2.0.
% Domain   : Syntactic
% Problem  : Goedel translation of SYN046+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    : GSY046+1 [QMLTP]

% Status   : CounterSatisfiable
% Rating   : 0.00 v8.2.0
% Syntax   : Number of formulae    :    7 (   1 unt;   5 typ;   0 def)
%            Number of atoms       :   23 (   0 equ)
%            Maximal formula atoms :   22 (  11 avg)
%            Number of connectives :   23 (   2   ~;   2   |;   1   &)
%                                         (   0 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   3 usr;   0 prp; 1-2 aty)
%            Number of functors    :    1 (   1 usr;   1 con; 0-0 aty)
%            Number of variables   :   16 (;  15   !;   1   ?;  16   :)
% 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(p_decl,type,
    p: '$ki_world' > $o ).

tff(q_decl,type,
    q: '$ki_world' > $o ).

tff(verify,conjecture,
    ( ! [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
       => ( ! [W0: '$ki_world'] :
              ( '$ki_accessible'(W,W0)
             => ( ! [W1: '$ki_world'] :
                    ( '$ki_accessible'(W0,W1)
                   => p(W1) )
               => ! [W1: '$ki_world'] :
                    ( '$ki_accessible'(W0,W1)
                   => q(W1) ) ) )
         => ( ! [W0: '$ki_world'] :
                ( '$ki_accessible'(W,W0)
               => ~ ! [W1: '$ki_world'] :
                      ( '$ki_accessible'(W0,W1)
                     => p(W1) ) )
            | ! [W0: '$ki_world'] :
                ( '$ki_accessible'(W,W0)
               => q(W0) ) ) ) )
    & ! [W: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',W)
       => ( ( ! [W0: '$ki_world'] :
                ( '$ki_accessible'(W,W0)
               => ~ ! [W1: '$ki_world'] :
                      ( '$ki_accessible'(W0,W1)
                     => p(W1) ) )
            | ! [W0: '$ki_world'] :
                ( '$ki_accessible'(W,W0)
               => q(W0) ) )
         => ! [W0: '$ki_world'] :
              ( '$ki_accessible'(W,W0)
             => ( ! [W1: '$ki_world'] :
                    ( '$ki_accessible'(W0,W1)
                   => p(W1) )
               => ! [W1: '$ki_world'] :
                    ( '$ki_accessible'(W0,W1)
                   => q(W1) ) ) ) ) ) ) ).

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