TPTP Problem File: LCL945^9.p
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%------------------------------------------------------------------------------
% File : LCL945^9 : TPTP v8.2.0. Released v8.1.0.
% Domain : Logic Calculi
% Problem : Goedel translation of NLP001+1 (from TPTP-v5.0.0)
% Version : [BP13] axioms.
% English :
% Refs : [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 : GNL001+1 [QMLTP]
% Status : Theorem
% Rating : 0.40 v8.2.0, 0.46 v8.1.0
% Syntax : Number of formulae : 41 ( 12 unt; 28 typ; 10 def)
% Number of atoms : 212 ( 10 equ; 0 cnn)
% Maximal formula atoms : 186 ( 16 avg)
% Number of connectives : 290 ( 1 ~; 1 |; 3 &; 281 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 4 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 90 ( 90 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 27 usr; 1 con; 0-3 aty)
% Number of variables : 47 ( 39 ^; 4 !; 4 ?; 47 :)
% 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 == $varying,
% $modalities == $modal_system_D].
%------------------------------------------------------------------------------
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_serial,axiom,
! [W: mworld] :
? [V: mworld] : ( mrel @ W @ V ) ).
thf(eiw_di_type,type,
eiw_di: $i > mworld > $o ).
thf(eiw_di_nonempty,axiom,
! [W: mworld] :
? [X: $i] : ( eiw_di @ X @ W ) ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] :
( ( eiw_di @ X @ W )
=> ( A @ X @ W ) ) ) ) ).
thf(mexists_di_type,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] :
( ( eiw_di @ X @ W )
& ( A @ X @ W ) ) ) ) ).
thf(chevy_decl,type,
chevy: $i > mworld > $o ).
thf(dirty_decl,type,
dirty: $i > mworld > $o ).
thf(barrel_decl,type,
barrel: $i > $i > mworld > $o ).
thf(hollywood_decl,type,
hollywood: $i > mworld > $o ).
thf(city_decl,type,
city: $i > mworld > $o ).
thf(in_decl,type,
in: $i > $i > mworld > $o ).
thf(old_decl,type,
old: $i > mworld > $o ).
thf(down_decl,type,
down: $i > $i > mworld > $o ).
thf(way_decl,type,
way: $i > mworld > $o ).
thf(white_decl,type,
white: $i > mworld > $o ).
thf(car_decl,type,
car: $i > mworld > $o ).
thf(street_decl,type,
street: $i > mworld > $o ).
thf(event_decl,type,
event: $i > mworld > $o ).
thf(lonely_decl,type,
lonely: $i > mworld > $o ).
thf(co1,conjecture,
( mlocal
@ ( mand
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [U: $i] :
( mexists_di
@ ^ [V: $i] :
( mexists_di
@ ^ [W: $i] :
( mexists_di
@ ^ [X: $i] : ( mand @ ( mbox @ ( hollywood @ U ) ) @ ( mand @ ( mbox @ ( city @ U ) ) @ ( mand @ ( mbox @ ( event @ V ) ) @ ( mand @ ( mbox @ ( street @ W ) ) @ ( mand @ ( mbox @ ( way @ W ) ) @ ( mand @ ( mbox @ ( lonely @ W ) ) @ ( mand @ ( mbox @ ( chevy @ X ) ) @ ( mand @ ( mbox @ ( car @ X ) ) @ ( mand @ ( mbox @ ( white @ X ) ) @ ( mand @ ( mbox @ ( dirty @ X ) ) @ ( mand @ ( mbox @ ( old @ X ) ) @ ( mand @ ( mbox @ ( barrel @ V @ X ) ) @ ( mand @ ( mbox @ ( down @ V @ W ) ) @ ( mbox @ ( in @ V @ U ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_di
@ ^ [Y: $i] :
( mexists_di
@ ^ [Z: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] : ( mand @ ( mbox @ ( hollywood @ Y ) ) @ ( mand @ ( mbox @ ( city @ Y ) ) @ ( mand @ ( mbox @ ( event @ Z ) ) @ ( mand @ ( mbox @ ( chevy @ X1 ) ) @ ( mand @ ( mbox @ ( car @ X1 ) ) @ ( mand @ ( mbox @ ( white @ X1 ) ) @ ( mand @ ( mbox @ ( dirty @ X1 ) ) @ ( mand @ ( mbox @ ( old @ X1 ) ) @ ( mand @ ( mbox @ ( street @ X2 ) ) @ ( mand @ ( mbox @ ( way @ X2 ) ) @ ( mand @ ( mbox @ ( lonely @ X2 ) ) @ ( mand @ ( mbox @ ( barrel @ Z @ X1 ) ) @ ( mand @ ( mbox @ ( down @ Z @ X2 ) ) @ ( mbox @ ( in @ Z @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mbox
@ ( mimplies
@ ( mexists_di
@ ^ [X3: $i] :
( mexists_di
@ ^ [X4: $i] :
( mexists_di
@ ^ [X5: $i] :
( mexists_di
@ ^ [X6: $i] : ( mand @ ( mbox @ ( hollywood @ X3 ) ) @ ( mand @ ( mbox @ ( city @ X3 ) ) @ ( mand @ ( mbox @ ( event @ X4 ) ) @ ( mand @ ( mbox @ ( chevy @ X5 ) ) @ ( mand @ ( mbox @ ( car @ X5 ) ) @ ( mand @ ( mbox @ ( white @ X5 ) ) @ ( mand @ ( mbox @ ( dirty @ X5 ) ) @ ( mand @ ( mbox @ ( old @ X5 ) ) @ ( mand @ ( mbox @ ( street @ X6 ) ) @ ( mand @ ( mbox @ ( way @ X6 ) ) @ ( mand @ ( mbox @ ( lonely @ X6 ) ) @ ( mand @ ( mbox @ ( barrel @ X4 @ X5 ) ) @ ( mand @ ( mbox @ ( down @ X4 @ X6 ) ) @ ( mbox @ ( in @ X4 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_di
@ ^ [X7: $i] :
( mexists_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X9: $i] :
( mexists_di
@ ^ [X10: $i] : ( mand @ ( mbox @ ( hollywood @ X7 ) ) @ ( mand @ ( mbox @ ( city @ X7 ) ) @ ( mand @ ( mbox @ ( event @ X8 ) ) @ ( mand @ ( mbox @ ( street @ X9 ) ) @ ( mand @ ( mbox @ ( way @ X9 ) ) @ ( mand @ ( mbox @ ( lonely @ X9 ) ) @ ( mand @ ( mbox @ ( chevy @ X10 ) ) @ ( mand @ ( mbox @ ( car @ X10 ) ) @ ( mand @ ( mbox @ ( white @ X10 ) ) @ ( mand @ ( mbox @ ( dirty @ X10 ) ) @ ( mand @ ( mbox @ ( old @ X10 ) ) @ ( mand @ ( mbox @ ( barrel @ X8 @ X10 ) ) @ ( mand @ ( mbox @ ( down @ X8 @ X9 ) ) @ ( mbox @ ( in @ X8 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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