%------------------------------------------------------------------------------
% File     : NLP267^2 : TPTP v8.2.0. Released v8.1.0.
% Domain   : Natural Language Processing
% Problem  : Ticket example
% Version  : [BP13] axioms.
% English  : 

% Refs     : [FH+98] Farinas del Cerro et al. (1998), Belief Reconstruction
%          : [RO12]  Raths & Otten (2012), The QMLTP Problem Library for Fi
%          : [BP13]  Benzmueller & Paulson (2013), Quantified Multimodal Lo
%          : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% Source   : [TPTP]
% Names    : APM001+1 [QMLTP]

% Status   : Theorem 
% Rating   : 0.10 v8.2.0, 0.23 v8.1.0
% Syntax   : Number of formulae    :   35 (   9 unt;  19 typ;   8 def)
%            Number of atoms       :   54 (   8 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   66 (   1   ~;   1   |;   2   &;  59   @)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   51 (  51   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   19 (  18 usr;   6 con; 0-3 aty)
%            Number of variables   :   22 (  19   ^;   2   !;   1   ?;  22   :)
% SPC      : TH0_THM_EQU_NAR

% Comments : This output was generated by embedproblem, version 1.7.1 (library
%            version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
%            'modal' embedding, version 1.5.2. Logic specification used:
%            $modal == [$constants == $rigid,$quantification == $constant,
%            $modalities == $modal_system_T].
%------------------------------------------------------------------------------
thf(mworld,type,
    mworld: $tType ).

thf(mrel_type,type,
    mrel: mworld > mworld > $o ).

thf(mactual_type,type,
    mactual: mworld ).

thf(mlocal_type,type,
    mlocal: ( mworld > $o ) > $o ).

thf(mlocal_def,definition,
    ( mlocal
    = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).

thf(mnot_type,type,
    mnot: ( mworld > $o ) > mworld > $o ).

thf(mand_type,type,
    mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mor_type,type,
    mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mimplies_type,type,
    mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mequiv_type,type,
    mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).

thf(mnot_def,definition,
    ( mnot
    = ( ^ [A: mworld > $o,W: mworld] :
          ~ ( A @ W ) ) ) ).

thf(mand_def,definition,
    ( mand
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          & ( B @ W ) ) ) ) ).

thf(mor_def,definition,
    ( mor
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
          | ( B @ W ) ) ) ) ).

thf(mimplies_def,definition,
    ( mimplies
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
         => ( B @ W ) ) ) ) ).

thf(mequiv_def,definition,
    ( mequiv
    = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
          ( ( A @ W )
        <=> ( B @ W ) ) ) ) ).

thf(mbox_type,type,
    mbox: ( mworld > $o ) > mworld > $o ).

thf(mbox_def,definition,
    ( mbox
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ! [V: mworld] :
          ( ( mrel @ W @ V )
         => ( Phi @ V ) ) ) ) ).

thf(mdia_type,type,
    mdia: ( mworld > $o ) > mworld > $o ).

thf(mdia_def,definition,
    ( mdia
    = ( ^ [Phi: mworld > $o,W: mworld] :
        ? [V: mworld] :
          ( ( mrel @ W @ V )
          & ( Phi @ V ) ) ) ) ).

thf(mrel_reflexive,axiom,
    ! [W: mworld] : ( mrel @ W @ W ) ).

thf(seventy_decl,type,
    seventy: $i ).

thf(ninetyfive_decl,type,
    ninetyfive: $i ).

thf(second_decl,type,
    second: $i ).

thf(paris_decl,type,
    paris: $i ).

thf(first_decl,type,
    first: $i ).

thf(price_decl,type,
    price: $i > mworld > $o ).

thf(dest_decl,type,
    dest: $i > mworld > $o ).

thf(class_decl,type,
    class: $i > mworld > $o ).

thf(law1,axiom,
    mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ first ) ) @ ( price @ ninetyfive ) ) ) ).

thf(law2,axiom,
    mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) ).

thf(law3,axiom,
    mlocal @ ( mbox @ ( mnot @ ( mand @ ( class @ first ) @ ( class @ second ) ) ) ) ).

thf(law4,axiom,
    mlocal @ ( mbox @ ( mnot @ ( mand @ ( price @ ninetyfive ) @ ( price @ seventy ) ) ) ) ).

thf(belief1,axiom,
    mlocal @ ( mbox @ ( dest @ paris ) ) ).

thf(belief2,axiom,
    mlocal @ ( mbox @ ( class @ second ) ) ).

thf(con,conjecture,
    mlocal @ ( mbox @ ( price @ seventy ) ) ).

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