%------------------------------------------------------------------------------
% File     : SWV430^1 : TPTP v8.2.0. 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   : 0.25 v8.2.0, 0.50 v8.1.0, 0.60 v7.5.0, 0.40 v7.4.0, 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 (  25 unt;  34 typ;  25 def)
%            Number of atoms       :   91 (  25 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :   71 (   3   ~;   1   |;   2   &;  64   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  132 ( 132   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   40 (  37 usr;   7 con; 0-3 aty)
%            Number of variables   :   49 (  41   ^;   4   !;   4   ?;  49   :)
% SPC      : TH0_CSA_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----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 ) ) ) ) ).

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