## TPTP Axioms File: LCL015^1.ax

```%------------------------------------------------------------------------------
% File     : LCL015^1 : TPTP v7.4.0. Released v5.5.0.
% Domain   : Logic Calculi (Quantified multimodal logic, cumulative domains)
% Axioms   : Cumulative domain specific axioms
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    :

% Status   : Satisfiable
% Syntax   : Number of formulae    :    1 (   0 unit;   0 type;   0 defn)
%            Number of atoms       :    9 (   0 equality;   6 variable)
%            Maximal formula depth :    8 (   8 average)
%            Number of connectives :    8 (   0   ~;   0   |;   1   &;   6   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&;   0  !!;   0  ??)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    4 (   0   :)
%            Number of variables   :    3 (   0 sgn;   3   !;   0   ?;   0   ^)
%                                         (   3   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : THF_SAT_EQU

% Comments : LCL015^0 and this are essentially LCL013^0.ax with the following
%            modifications to support cumulative domains:
%            - addition of a predicate exists_in_world
%            - use of this predicate in a modified definition mforall_ind
%            - use of this predicate in an added axiom for cumulative domains
%          : Requires LCL015^0 LCL013^5
%------------------------------------------------------------------------------
thf(cumulative_ax,axiom,(
! [X: mu,V: \$i,W: \$i] :
( ( ( exists_in_world @ X @ V )
& ( rel_s4 @ V @ W ) )
=> ( exists_in_world @ X @ W ) ) )).

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