TPTP Problem File: SYO903^10.p
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%------------------------------------------------------------------------------
% File : SYO903^10 : TPTP v8.2.0. Released v8.1.0.
% Domain : Syntactic
% Problem : PSAT - CNF - K=4 C=50 V=4 D=2.8
% 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 : SYM329+1 [QMLTP]
% Status : ContradictoryAxioms
% Rating : 0.20 v8.2.0, 0.31 v8.1.0
% Syntax : Number of formulae : 77 ( 9 unt; 15 typ; 8 def)
% Number of atoms : 713 ( 8 equ; 0 cnn)
% Maximal formula atoms : 17 ( 11 avg)
% Number of connectives : 672 ( 1 ~; 1 |; 3 &; 663 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 3 con; 0-3 aty)
% Number of variables : 27 ( 21 ^; 5 !; 1 ?; 27 :)
% 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 == $varying,
% $modalities == $modal_system_S4].
%------------------------------------------------------------------------------
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_transitive,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ V )
& ( mrel @ V @ U ) )
=> ( mrel @ W @ U ) ) ).
thf(v1_decl,type,
v1: mworld > $o ).
thf(v2_decl,type,
v2: mworld > $o ).
thf(v3_decl,type,
v3: mworld > $o ).
thf(v4_decl,type,
v4: mworld > $o ).
thf(persat1,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ v3 @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat2,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
thf(persat3,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat4,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
thf(persat5,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v3 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat6,axiom,
mlocal @ ( mor @ v1 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat7,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
thf(persat8,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
thf(persat9,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v4 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat10,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat11,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat12,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat13,axiom,
mlocal @ ( mor @ v1 @ ( mor @ ( mbox @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
thf(persat14,axiom,
mlocal @ ( mor @ v2 @ ( mor @ v3 @ ( mor @ v4 @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat15,axiom,
mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat16,axiom,
mlocal @ ( mor @ v2 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
thf(persat17,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
thf(persat18,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat19,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
thf(persat20,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
thf(persat21,axiom,
mlocal @ ( mor @ v2 @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat22,axiom,
mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ v2 ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
thf(persat23,axiom,
mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat24,axiom,
mlocal @ ( mor @ v3 @ ( mor @ v4 @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat25,axiom,
mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
thf(persat26,axiom,
mlocal @ ( mor @ v3 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat27,axiom,
mlocal @ ( mor @ v3 @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat28,axiom,
mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) ) ) ) ).
thf(persat29,axiom,
mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
thf(persat30,axiom,
mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v1 ) @ ( mbox @ ( mbox @ v2 ) ) ) ) ) ).
thf(persat31,axiom,
mlocal @ ( mor @ v4 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat32,axiom,
mlocal @ ( mor @ v4 @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat33,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v3 ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat34,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat35,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat36,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
thf(persat37,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat38,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat39,axiom,
mlocal @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
thf(persat40,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v1 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat41,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
thf(persat42,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v3 ) ) ) ) ) ) ).
thf(persat43,axiom,
mlocal @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v1 ) ) ) ) ) ) ).
thf(persat44,axiom,
mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat45,axiom,
mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mbox @ ( mbox @ v3 ) ) ) ) ) ).
thf(persat46,axiom,
mlocal @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox @ ( mnot @ v4 ) ) @ ( mor @ ( mbox @ ( mbox @ ( mnot @ v2 ) ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat47,axiom,
mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v1 ) @ ( mor @ ( mbox @ ( mbox @ v3 ) ) @ ( mbox @ ( mbox @ v4 ) ) ) ) ) ).
thf(persat48,axiom,
mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v3 ) @ ( mor @ ( mbox @ ( mbox @ v2 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(persat49,axiom,
mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v1 ) ) @ ( mbox @ ( mbox @ v1 ) ) ) ) ) ).
thf(persat50,axiom,
mlocal @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox @ ( mnot @ v2 ) ) @ ( mor @ ( mbox @ ( mbox @ v4 ) ) @ ( mbox @ ( mbox @ ( mnot @ v4 ) ) ) ) ) ) ).
thf(deontic1,axiom,
( mlocal
@ ( mdia
@ ^ [W: mworld] : $true ) ) ).
thf(result1,conjecture,
( mlocal
@ ^ [W: mworld] : $false ) ).
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