TPTP Problem File: NLP266^23.p
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%------------------------------------------------------------------------------
% File : NLP266^23 : TPTP v8.2.0. Released v8.1.0.
% Domain : Natural Language Processing
% Problem : Generation of abstract instructions: enter a number in a box
% Version : [BP13] axioms.
% English :
% Refs : [Sto00] Stone (2000), Towards a Computational Account of Knowl
% : [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 : APM003+1 [QMLTP]
% Status : Theorem
% Rating : 0.60 v8.2.0, 0.77 v8.1.0
% Syntax : Number of formulae : 40 ( 12 unt; 22 typ; 10 def)
% Number of atoms : 78 ( 10 equ; 0 cnn)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 120 ( 1 ~; 1 |; 5 &; 107 @)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 21 usr; 3 con; 0-4 aty)
% Number of variables : 48 ( 35 ^; 10 !; 3 ?; 48 :)
% 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 == $decreasing,
% $modalities == $modal_system_S5].
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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(mrel_euclidean,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ 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(eiw_di_decr,axiom,
! [W: mworld,V: mworld,X: $i] :
( ( ( eiw_di @ X @ W )
& ( mrel @ V @ W ) )
=> ( eiw_di @ X @ V ) ) ).
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(u_decl,type,
u: $i ).
thf(one_decl,type,
one: $i ).
thf(number_decl,type,
number: $i > $i > mworld > $o ).
thf(string_decl,type,
string: $i > mworld > $o ).
thf(in_decl,type,
in: $i > $i > $i > mworld > $o ).
thf(do_decl,type,
do: $i > $i > $i > mworld > $o ).
thf(entry_box_decl,type,
entry_box: $i > mworld > $o ).
thf(userid_decl,type,
userid: $i > $i > mworld > $o ).
thf(ax1,axiom,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [I: $i] : ( mbox @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
thf(ax2,axiom,
( mlocal
@ ( mexists_di
@ ^ [B: $i] : ( mbox @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
thf(ax3,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [S: $i] :
( mforall_di
@ ^ [I: $i] :
( mforall_di
@ ^ [B: $i] :
( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
@ ( mexists_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(con,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [I: $i] :
( mexists_di
@ ^ [B: $i] :
( mexists_di
@ ^ [A: $i] :
( mexists_di
@ ^ [S: $i] :
( mand @ ( mbox @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [S2: $i] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
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