TPTP Problem File: NLP265^17.p
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% File : NLP265^17 : TPTP v8.2.0. Released v8.1.0.
% Domain : Natural Language Processing
% Problem : Schema instantiation example
% Version : [BP13] axioms.
% English : Alice intends Bob to believe that Portland is a big city.
% Refs : [BS96] Bretier & Sadek (1996), Rational Agent as the Kernel o
% : [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 : MML014+1 [QMLTP]
% Status : ContradictoryAxioms
% Rating : 0.10 v8.2.0, 0.23 v8.1.0
% Syntax : Number of formulae : 39 ( 12 unt; 18 typ; 8 def)
% Number of atoms : 70 ( 8 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 136 ( 1 ~; 1 |; 6 &; 121 @)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 39 ( 21 ^; 17 !; 1 ?; 39 :)
% SPC : TH0_CAX_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 == $cumulative,
% $modalities == $modal_system_S5].
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thf(mworld,type,
mworld: $tType ).
thf(mindex,type,
mindex: $tType ).
thf(mrel_type,type,
mrel: mindex > mworld > mworld > $o ).
thf('#i_alice_type',type,
'#i_alice': mindex ).
thf('#i_bob_type',type,
'#i_bob': mindex ).
thf('#b_alice_type',type,
'#b_alice': mindex ).
thf('#b_bob_type',type,
'#b_bob': mindex ).
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: mindex > ( mworld > $o ) > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ R @ W @ V )
=> ( Phi @ V ) ) ) ) ).
thf(mdia_type,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [R: mindex,Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ R @ W @ V )
& ( Phi @ V ) ) ) ) ).
thf('mrel_#i_alice_reflexive',axiom,
! [W: mworld] : ( mrel @ '#i_alice' @ W @ W ) ).
thf('mrel_#i_alice_euclidean',axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ '#i_alice' @ W @ U )
& ( mrel @ '#i_alice' @ W @ V ) )
=> ( mrel @ '#i_alice' @ U @ V ) ) ).
thf('mrel_#i_bob_reflexive',axiom,
! [W: mworld] : ( mrel @ '#i_bob' @ W @ W ) ).
thf('mrel_#i_bob_euclidean',axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ '#i_bob' @ W @ U )
& ( mrel @ '#i_bob' @ W @ V ) )
=> ( mrel @ '#i_bob' @ U @ V ) ) ).
thf('mrel_#b_alice_reflexive',axiom,
! [W: mworld] : ( mrel @ '#b_alice' @ W @ W ) ).
thf('mrel_#b_alice_euclidean',axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ '#b_alice' @ W @ U )
& ( mrel @ '#b_alice' @ W @ V ) )
=> ( mrel @ '#b_alice' @ U @ V ) ) ).
thf('mrel_#b_bob_reflexive',axiom,
! [W: mworld] : ( mrel @ '#b_bob' @ W @ W ) ).
thf('mrel_#b_bob_euclidean',axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ '#b_bob' @ W @ U )
& ( mrel @ '#b_bob' @ W @ V ) )
=> ( mrel @ '#b_bob' @ U @ V ) ) ).
thf(portland_decl,type,
portland: $i ).
thf(bigcity_decl,type,
bigcity: $i > mworld > $o ).
thf(axiom_1_alice,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ) ) ).
thf(axiom_1_bob,axiom,
mlocal @ ( mbox @ '#b_bob' @ ( mimplies @ ( mand @ ( bigcity @ portland ) @ ( mbox @ '#b_bob' @ ( mbox @ '#b_alice' @ ( mnot @ ( bigcity @ portland ) ) ) ) ) @ ( mbox @ '#i_bob' @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ) ) ) ).
thf(axiom_2,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) ).
thf(axiom_3,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) ).
thf(con,conjecture,
mlocal @ ( mbox @ '#i_alice' @ ( mbox @ '#b_bob' @ ( bigcity @ portland ) ) ) ).
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