## TPTP Problem File: SWV442^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWV442^1 : TPTP v8.1.2. Released v3.7.0.
% Domain   : Software Verification (Security)
% Problem  : A => A in BL
% Version  : [Gar08] axioms.
% English  :

% Refs     : [AM+01] Alechina et al. (2001), Categorical and Kripke Semanti
%          : [Gar08] Garg (2008), Principal-Centric Reasoning in Constructi
%          : [Gar09] Garg (2009), Email to Geoff Sutcliffe
% Source   : [Gar09]
% Names    :

% Status   : Theorem
% Rating   : 0.23 v8.1.0, 0.18 v7.5.0, 0.29 v7.4.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0, 0.33 v3.7.0
% Syntax   : Number of formulae    :   84 (  34 unt;  43 typ;  34 def)
%            Number of atoms       :  148 (  34 equ;   0 cnn)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  117 (   3   ~;   1   |;   2   &; 110   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  175 ( 175   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   48 (  45 usr;   7 con; 0-3 aty)
%            Number of variables   :   64 (  50   ^  10   !;   4   ?;  64   :)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include axioms of multi-modal logic
include('Axioms/LCL008^0.ax').
%----Include axioms translating constructive S4 (CS4) to bimodal classical
%----S4 (BS4)
include('Axioms/LCL009^0.ax').
%----Include axioms for translation from Binder Logic (BL) to CS4
include('Axioms/SWV010^0.ax').
%------------------------------------------------------------------------------
thf(bl_id,conjecture,
! [A: \$i > \$o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ A ) @ ( bl_atom @ A ) ) ) ).

%------------------------------------------------------------------------------
```