TPTP Problem File: NLP004^8.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : NLP004^8 : TPTP v8.2.0. Released v8.1.0.
% Domain : Natural Language Processing
% Problem : "The old dirty white Chevy" problem 4
% 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 : NLP004+1 [QMLTP]
% Status : Theorem
% Rating : 0.60 v8.2.0, 0.62 v8.1.0
% Syntax : Number of formulae : 74 ( 12 unt; 35 typ; 10 def)
% Number of atoms : 526 ( 10 equ; 0 cnn)
% Maximal formula atoms : 292 ( 13 avg)
% Number of connectives : 782 ( 1 ~; 1 |; 3 &; 773 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 10 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 105 ( 105 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 34 usr; 1 con; 0-3 aty)
% Number of variables : 128 ( 121 ^; 4 !; 3 ?; 128 :)
% 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_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(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(young_decl,type,
young: $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(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(seat_decl,type,
seat: $i > mworld > $o ).
thf(white_decl,type,
white: $i > mworld > $o ).
thf(car_decl,type,
car: $i > mworld > $o ).
thf(furniture_decl,type,
furniture: $i > mworld > $o ).
thf(street_decl,type,
street: $i > mworld > $o ).
thf(fellow_decl,type,
fellow: $i > mworld > $o ).
thf(front_decl,type,
front: $i > mworld > $o ).
thf(man_decl,type,
man: $i > mworld > $o ).
thf(event_decl,type,
event: $i > mworld > $o ).
thf(lonely_decl,type,
lonely: $i > mworld > $o ).
thf(reflexivity,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
thf(symmetry,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
thf(transitivity,axiom,
( mlocal
@ ( mforall_di
@ ^ [X: $i] :
( mforall_di
@ ^ [Y: $i] :
( mforall_di
@ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
thf(barrel_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( barrel @ A @ C ) ) @ ( barrel @ B @ C ) ) ) ) ) ) ).
thf(barrel_substitution_2,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( barrel @ C @ A ) ) @ ( barrel @ C @ B ) ) ) ) ) ) ).
thf(car_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( car @ A ) ) @ ( car @ B ) ) ) ) ) ).
thf(chevy_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( chevy @ A ) ) @ ( chevy @ B ) ) ) ) ) ).
thf(city_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( city @ A ) ) @ ( city @ B ) ) ) ) ) ).
thf(dirty_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( dirty @ A ) ) @ ( dirty @ B ) ) ) ) ) ).
thf(down_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( down @ A @ C ) ) @ ( down @ B @ C ) ) ) ) ) ) ).
thf(down_substitution_2,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( down @ C @ A ) ) @ ( down @ C @ B ) ) ) ) ) ) ).
thf(event_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( event @ A ) ) @ ( event @ B ) ) ) ) ) ).
thf(fellow_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( fellow @ A ) ) @ ( fellow @ B ) ) ) ) ) ).
thf(front_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( front @ A ) ) @ ( front @ B ) ) ) ) ) ).
thf(furniture_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( furniture @ A ) ) @ ( furniture @ B ) ) ) ) ) ).
thf(hollywood_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( hollywood @ A ) ) @ ( hollywood @ B ) ) ) ) ) ).
thf(in_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
thf(in_substitution_2,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] :
( mforall_di
@ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
thf(lonely_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( lonely @ A ) ) @ ( lonely @ B ) ) ) ) ) ).
thf(man_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( man @ A ) ) @ ( man @ B ) ) ) ) ) ).
thf(old_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( old @ A ) ) @ ( old @ B ) ) ) ) ) ).
thf(seat_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( seat @ A ) ) @ ( seat @ B ) ) ) ) ) ).
thf(street_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( street @ A ) ) @ ( street @ B ) ) ) ) ) ).
thf(way_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( way @ A ) ) @ ( way @ B ) ) ) ) ) ).
thf(white_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( white @ A ) ) @ ( white @ B ) ) ) ) ) ).
thf(young_substitution_1,axiom,
( mlocal
@ ( mforall_di
@ ^ [A: $i] :
( mforall_di
@ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( young @ A ) ) @ ( young @ B ) ) ) ) ) ).
thf(co1,conjecture,
( mlocal
@ ( mand
@ ( mimplies
@ ( mexists_di
@ ^ [U: $i] :
( mexists_di
@ ^ [V: $i] :
( mexists_di
@ ^ [W: $i] :
( mexists_di
@ ^ [X: $i] :
( mexists_di
@ ^ [Y: $i] :
( mexists_di
@ ^ [Z: $i] :
( mexists_di
@ ^ [X1: $i] :
( mexists_di
@ ^ [X2: $i] :
( mexists_di
@ ^ [X4: $i] :
( mexists_di
@ ^ [X5: $i] : ( mand @ ( seat @ U ) @ ( mand @ ( furniture @ U ) @ ( mand @ ( front @ U ) @ ( mand @ ( seat @ V ) @ ( mand @ ( furniture @ V ) @ ( mand @ ( front @ V ) @ ( mand @ ( hollywood @ W ) @ ( mand @ ( city @ W ) @ ( mand @ ( event @ X ) @ ( mand @ ( street @ Y ) @ ( mand @ ( way @ Y ) @ ( mand @ ( lonely @ Y ) @ ( mand @ ( chevy @ Z ) @ ( mand @ ( car @ Z ) @ ( mand @ ( white @ Z ) @ ( mand @ ( dirty @ Z ) @ ( mand @ ( old @ Z ) @ ( mand @ ( barrel @ X @ Z ) @ ( mand @ ( down @ X @ Y ) @ ( mand @ ( in @ X @ W ) @ ( mand @ ( mnot @ ( qmltpeq @ X1 @ X2 ) ) @ ( mand @ ( fellow @ X1 ) @ ( mand @ ( man @ X1 ) @ ( mand @ ( young @ X1 ) @ ( mand @ ( fellow @ X2 ) @ ( mand @ ( man @ X2 ) @ ( mand @ ( young @ X2 ) @ ( mand @ ( qmltpeq @ X1 @ X4 ) @ ( mand @ ( in @ X4 @ U ) @ ( mand @ ( qmltpeq @ X2 @ X5 ) @ ( in @ X5 @ V ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_di
@ ^ [X6: $i] :
( mexists_di
@ ^ [X7: $i] :
( mexists_di
@ ^ [X8: $i] :
( mexists_di
@ ^ [X9: $i] :
( mexists_di
@ ^ [X10: $i] :
( mexists_di
@ ^ [X11: $i] :
( mexists_di
@ ^ [X12: $i] :
( mexists_di
@ ^ [X13: $i] :
( mexists_di
@ ^ [X15: $i] :
( mexists_di
@ ^ [X16: $i] : ( mand @ ( seat @ X6 ) @ ( mand @ ( furniture @ X6 ) @ ( mand @ ( front @ X6 ) @ ( mand @ ( seat @ X7 ) @ ( mand @ ( furniture @ X7 ) @ ( mand @ ( front @ X7 ) @ ( mand @ ( hollywood @ X8 ) @ ( mand @ ( city @ X8 ) @ ( mand @ ( event @ X9 ) @ ( mand @ ( chevy @ X10 ) @ ( mand @ ( car @ X10 ) @ ( mand @ ( white @ X10 ) @ ( mand @ ( dirty @ X10 ) @ ( mand @ ( old @ X10 ) @ ( mand @ ( street @ X11 ) @ ( mand @ ( way @ X11 ) @ ( mand @ ( lonely @ X11 ) @ ( mand @ ( barrel @ X9 @ X10 ) @ ( mand @ ( down @ X9 @ X11 ) @ ( mand @ ( in @ X9 @ X8 ) @ ( mand @ ( mnot @ ( qmltpeq @ X12 @ X13 ) ) @ ( mand @ ( fellow @ X12 ) @ ( mand @ ( man @ X12 ) @ ( mand @ ( young @ X12 ) @ ( mand @ ( fellow @ X13 ) @ ( mand @ ( man @ X13 ) @ ( mand @ ( young @ X13 ) @ ( mand @ ( qmltpeq @ X12 @ X15 ) @ ( mand @ ( in @ X15 @ X6 ) @ ( mand @ ( qmltpeq @ X13 @ X16 ) @ ( in @ X16 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mimplies
@ ( mexists_di
@ ^ [X17: $i] :
( mexists_di
@ ^ [X18: $i] :
( mexists_di
@ ^ [X19: $i] :
( mexists_di
@ ^ [X20: $i] :
( mexists_di
@ ^ [X21: $i] :
( mexists_di
@ ^ [X22: $i] :
( mexists_di
@ ^ [X23: $i] :
( mexists_di
@ ^ [X24: $i] :
( mexists_di
@ ^ [X26: $i] :
( mexists_di
@ ^ [X27: $i] : ( mand @ ( seat @ X17 ) @ ( mand @ ( furniture @ X17 ) @ ( mand @ ( front @ X17 ) @ ( mand @ ( seat @ X18 ) @ ( mand @ ( furniture @ X18 ) @ ( mand @ ( front @ X18 ) @ ( mand @ ( hollywood @ X19 ) @ ( mand @ ( city @ X19 ) @ ( mand @ ( event @ X20 ) @ ( mand @ ( chevy @ X21 ) @ ( mand @ ( car @ X21 ) @ ( mand @ ( white @ X21 ) @ ( mand @ ( dirty @ X21 ) @ ( mand @ ( old @ X21 ) @ ( mand @ ( street @ X22 ) @ ( mand @ ( way @ X22 ) @ ( mand @ ( lonely @ X22 ) @ ( mand @ ( barrel @ X20 @ X21 ) @ ( mand @ ( down @ X20 @ X22 ) @ ( mand @ ( in @ X20 @ X19 ) @ ( mand @ ( mnot @ ( qmltpeq @ X23 @ X24 ) ) @ ( mand @ ( fellow @ X23 ) @ ( mand @ ( man @ X23 ) @ ( mand @ ( young @ X23 ) @ ( mand @ ( fellow @ X24 ) @ ( mand @ ( man @ X24 ) @ ( mand @ ( young @ X24 ) @ ( mand @ ( qmltpeq @ X23 @ X26 ) @ ( mand @ ( in @ X26 @ X17 ) @ ( mand @ ( qmltpeq @ X24 @ X27 ) @ ( in @ X27 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_di
@ ^ [X28: $i] :
( mexists_di
@ ^ [X29: $i] :
( mexists_di
@ ^ [X30: $i] :
( mexists_di
@ ^ [X31: $i] :
( mexists_di
@ ^ [X32: $i] :
( mexists_di
@ ^ [X33: $i] :
( mexists_di
@ ^ [X34: $i] :
( mexists_di
@ ^ [X35: $i] :
( mexists_di
@ ^ [X37: $i] :
( mexists_di
@ ^ [X38: $i] : ( mand @ ( seat @ X28 ) @ ( mand @ ( furniture @ X28 ) @ ( mand @ ( front @ X28 ) @ ( mand @ ( seat @ X29 ) @ ( mand @ ( furniture @ X29 ) @ ( mand @ ( front @ X29 ) @ ( mand @ ( hollywood @ X30 ) @ ( mand @ ( city @ X30 ) @ ( mand @ ( event @ X31 ) @ ( mand @ ( street @ X32 ) @ ( mand @ ( way @ X32 ) @ ( mand @ ( lonely @ X32 ) @ ( mand @ ( chevy @ X33 ) @ ( mand @ ( car @ X33 ) @ ( mand @ ( white @ X33 ) @ ( mand @ ( dirty @ X33 ) @ ( mand @ ( old @ X33 ) @ ( mand @ ( barrel @ X31 @ X33 ) @ ( mand @ ( down @ X31 @ X32 ) @ ( mand @ ( in @ X31 @ X30 ) @ ( mand @ ( mnot @ ( qmltpeq @ X34 @ X35 ) ) @ ( mand @ ( fellow @ X34 ) @ ( mand @ ( man @ X34 ) @ ( mand @ ( young @ X34 ) @ ( mand @ ( fellow @ X35 ) @ ( mand @ ( man @ X35 ) @ ( mand @ ( young @ X35 ) @ ( mand @ ( qmltpeq @ X34 @ X37 ) @ ( mand @ ( in @ X37 @ X28 ) @ ( mand @ ( qmltpeq @ X35 @ X38 ) @ ( in @ X38 @ X29 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------