%------------------------------------------------------------------------------
% File     : SWC425^7 : TPTP v8.2.0. Released v5.5.0.
% Domain   : Software Creation
% Problem  : Conflict detection of 2 conceptual schemata (e.g. UML-schemata)
% Version  : [Ben12] axioms.
% English  :

% Refs     : [BE04]  Boeva & Ekenberg (2004), A Transition Logic for Schema
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-APM002+1 [Ben12]

% Status   : CounterSatisfiable
% Rating   : 0.75 v8.2.0, 1.00 v8.1.0, 0.60 v7.5.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v6.0.0, 0.67 v5.5.0
% Syntax   : Number of formulae    :   84 (  36 unt;  41 typ;  32 def)
%            Number of atoms       :  157 (  36 equ;   0 cnn)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  214 (   5   ~;   5   |;   9   &; 185   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   2 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  184 ( 184   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   52 (  50 usr;  14 con; 0-3 aty)
%            Number of variables   :   94 (  50   ^;  37   !;   7   ?;  94   :)
% SPC      : TH0_CSA_EQU_NAR

% Comments : 
%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(r_type,type,
    r: mu > $i > $o ).

thf(p_type,type,
    p: mu > $i > $o ).

thf(c_type,type,
    c: mu ).

thf(existence_of_c_ax,axiom,
    ! [V: $i] : ( exists_in_world @ c @ V ) ).

thf(b_type,type,
    b: mu ).

thf(existence_of_b_ax,axiom,
    ! [V: $i] : ( exists_in_world @ b @ V ) ).

thf(a_type,type,
    a: mu ).

thf(existence_of_a_ax,axiom,
    ! [V: $i] : ( exists_in_world @ a @ V ) ).

thf(schema1,axiom,
    mvalid @ ( mand @ ( mor @ ( mnot @ ( r @ a ) ) @ ( r @ b ) ) @ ( mand @ ( mequiv @ ( r @ c ) @ ( r @ a ) ) @ ( mand @ ( mimplies @ ( r @ a ) @ ( mdia_s4 @ ( r @ b ) ) ) @ ( mimplies @ ( mnot @ ( r @ a ) ) @ ( mdia_s4 @ ( mand @ ( mnot @ ( r @ b ) ) @ ( mnot @ ( r @ c ) ) ) ) ) ) ) ) ).

thf(schema2,axiom,
    mvalid @ ( mand @ ( mimplies @ ( p @ a ) @ ( p @ b ) ) @ ( mand @ ( mor @ ( p @ c ) @ ( mnot @ ( p @ b ) ) ) @ ( mimplies @ ( mand @ ( p @ a ) @ ( p @ b ) ) @ ( mdia_s4 @ ( mnot @ ( p @ b ) ) ) ) ) ) ).

thf(integration_assertion,axiom,
    ( mvalid
    @ ( mforall_ind
      @ ^ [X: mu] : ( mequiv @ ( p @ X ) @ ( r @ X ) ) ) ) ).

thf(con,conjecture,
    mvalid @ mfalse ).

%------------------------------------------------------------------------------