## TPTP Axioms File: LCL015^1.ax

```%------------------------------------------------------------------------------
% File     : LCL015^1 : TPTP v8.1.0. 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 unt;   0 typ;   0 def)
%            Number of atoms       :    3 (   0 equ;   0 cnn)
%            Maximal formula atoms :    3 (   3 avg)
%            Number of connectives :    8 (   0   ~;   0   |;   1   &;   6   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   8 avg;   6 nst)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :    3 (   0   ^   3   !;   0   ?;   3   :)
% 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 ) ) ).

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