TPTP Problem File: PUZ150^18.p
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%------------------------------------------------------------------------------
% File : PUZ150^18 : TPTP v8.2.0. Released v8.1.0.
% Domain : Puzzles
% Problem : Russian card problem (very simple variant)
% Version : [BP13] axioms.
% English : Anne, Bill and Cath draw 0, 1, and 2. Anne knows that Bill knows
% that Cath knows her own card, etc. Anne has card 0. Then Bill
% knows that Anne does not consider it possible that Bill considers
% it possible that Cath knows that Anne does not have card 0.
% Refs : [vDK06] van Ditmarsch & Kooi (2006), The Secret of My Success
% : [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 : MML007+1 [QMLTP]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.31 v8.1.0
% Syntax : Number of formulae : 45 ( 11 unt; 25 typ; 8 def)
% Number of atoms : 108 ( 8 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 151 ( 1 ~; 1 |; 2 &; 144 @)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 23 usr; 4 con; 0-3 aty)
% Number of variables : 29 ( 21 ^; 7 !; 1 ?; 29 :)
% 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 == $cumulative,
% $modalities == $modal_system_S5U].
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thf(mworld,type,
mworld: $tType ).
thf(mindex,type,
mindex: $tType ).
thf(mrel_type,type,
mrel: mindex > mworld > mworld > $o ).
thf('#c_type',type,
'#c': mindex ).
thf('#b_type',type,
'#b': mindex ).
thf('#a_type',type,
'#a': 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_#c_universal',axiom,
! [W: mworld,V: mworld] : ( mrel @ '#c' @ W @ V ) ).
thf('mrel_#b_universal',axiom,
! [W: mworld,V: mworld] : ( mrel @ '#b' @ W @ V ) ).
thf('mrel_#a_universal',axiom,
! [W: mworld,V: mworld] : ( mrel @ '#a' @ W @ V ) ).
%%% This output was generated by tptputils, version 1.2.
%%% Generated on Wed Apr 27 15:49:37 CEST 2022 using command 'downgrade(tff)'.
thf(c0_decl,type,
c0: mworld > $o ).
thf(c1_decl,type,
c1: mworld > $o ).
thf(b0_decl,type,
b0: mworld > $o ).
thf(c2_decl,type,
c2: mworld > $o ).
thf(b1_decl,type,
b1: mworld > $o ).
thf(a0_decl,type,
a0: mworld > $o ).
thf(b2_decl,type,
b2: mworld > $o ).
thf(a1_decl,type,
a1: mworld > $o ).
thf(a2_decl,type,
a2: mworld > $o ).
thf(cb_decl,type,
cb: mworld > $o ).
thf(axiom_knows_a_b_c,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
thf(axiom_knows_b_a_c,axiom,
mlocal @ ( mbox @ '#b' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
thf(axiom_knows_a_b_c_0,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#c' @ c0 ) @ ( mor @ ( mbox @ '#c' @ c1 ) @ ( mbox @ '#c' @ c2 ) ) ) ) ) ).
thf(axiom_knows_a_c_b,axiom,
mlocal @ ( mbox @ '#a' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#b' @ b0 ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ) ).
thf(axiom_knows_c_a_b,axiom,
mlocal @ ( mbox @ '#c' @ ( mbox @ '#a' @ ( mor @ ( mbox @ '#b' @ cb ) @ ( mor @ ( mbox @ '#b' @ b1 ) @ ( mbox @ '#b' @ b2 ) ) ) ) ) ).
thf(axiom_knows_c_b_a,axiom,
mlocal @ ( mbox @ '#c' @ ( mbox @ '#b' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ) ).
thf(axiom_knows_b_c_a,axiom,
mlocal @ ( mbox @ '#b' @ ( mbox @ '#c' @ ( mor @ ( mbox @ '#a' @ a0 ) @ ( mor @ ( mbox @ '#a' @ a1 ) @ ( mbox @ '#a' @ a2 ) ) ) ) ) ).
thf(axiom_a0,axiom,
mlocal @ a0 ).
thf(con,conjecture,
mlocal @ ( mbox @ '#b' @ ( mnot @ ( mdia @ '#a' @ ( mdia @ '#b' @ ( mbox @ '#c' @ ( mnot @ a0 ) ) ) ) ) ) ).
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