## TPTP Problem File: SWV430^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWV430^1 : TPTP v7.2.0. Released v3.6.0.
% Domain   : Software Verification (Security)
% Problem  : ICL^=> logic mapping to modal logic implies 'trans'
% Version  : [Ben08] axioms.
% 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   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v6.2.0, 0.00 v4.0.0, 1.00 v3.7.0
% Syntax   : Number of formulae    :   60 (   0 unit;  34 type;  25 defn)
%            Number of atoms       :  144 (  25 equality;  53 variable)
%            Maximal formula depth :    9 (   5 average)
%            Number of connectives :   71 (   3   ~;   1   |;   2   &;  64   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  132 ( 132   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   39 (  34   :;   0   =)
%            Number of variables   :   49 (   2 sgn;   4   !;   4   ?;  41   ^)
%                                         (  49   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_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 of ICL^=> logic
include('Axioms/SWV008^2.ax').
%------------------------------------------------------------------------------
%----We introduce an arbitrary principal a
thf(a,type,(
a: \$i > \$o )).

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

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

%----Can we prove 'trans'?
thf(trans,conjecture,
( iclval @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ b ) ) @ ( icl_impl @ ( icl_impl_princ @ ( icl_princ @ b ) @ ( icl_princ @ c ) ) @ ( icl_impl_princ @ ( icl_princ @ a ) @ ( icl_princ @ c ) ) ) ) )).

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