## TPTP Problem File: SWV426^4.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWV426^4 : TPTP v7.1.0. Released v3.6.0.
% Domain   : Software Verification (Security)
% Problem  : ICL^B logic mapping to modal logic implies 'cuc'
% Version  : [Ben08] axioms : Augmented.
% English  :

% Refs     : [GA08]  Garg & Abadi (2008), A Modal Deconstruction of Access
%          : [Ben08] Benzmueller (2008), Automating Access Control Logics i
%          : [BP09]  Benzmueller & Paulson (2009), Exploring Properties of
% Source   : [Ben08]
% Names    :

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.67 v3.7.0
% Syntax   : Number of formulae    :   60 (   0 unit;  33 type;  24 defn)
%            Number of atoms       :  156 (  24 equality;  55 variable)
%            Maximal formula depth :    9 (   5 average)
%            Number of connectives :   84 (   3   ~;   1   |;   2   &;  77   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  127 ( 127   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   38 (  33   :;   0   =)
%            Number of variables   :   49 (   2 sgn;   6   !;   4   ?;  39   ^)
%                                         (  49   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include axioms of multi modal logic
include('Axioms/LCL008^0.ax').
%----Include axioms of ICL logic
include('Axioms/SWV008^0.ax').
%----Include axioms for ICL notions of validity wrt S4
include('Axioms/SWV008^1.ax').
%------------------------------------------------------------------------------
%----We introduce an arbitrary atom s
thf(s,type,(
s: \$i > \$o )).

%----We introduce the arbitrary principals a and b
thf(a,type,(
a: \$i > \$o )).

thf(b,type,(
b: \$i > \$o )).

%----Can we prove 'cuc''?
thf(cuc,conjecture,
( iclval @ ( icl_impl @ ( icl_says @ ( icl_impl @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_atom @ s ) ) @ ( icl_impl @ ( icl_says @ ( icl_princ @ a ) @ ( icl_atom @ s ) ) @ ( icl_says @ ( icl_princ @ b ) @ ( icl_atom @ s ) ) ) ) )).

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