## TPTP Problem File: SYO571^7.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO571^7 : TPTP v7.2.0. Released v5.5.0.
% Domain   : Syntactic
% Problem  : Quantified modal logics wwfs. problem 9.
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Sid09] Sider (2009), Logic for Philosophy
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-SYM070+1 [Ben12]

% Status   : CounterSatisfiable
% Rating   : 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    :   75 (   0 unit;  37 type;  32 defn)
%            Number of atoms       :  258 (  36 equality; 145 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  153 (   5   ~;   5   |;   9   &; 124   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  180 ( 180   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  37   :;   0   =)
%            Number of variables   :   92 (   2 sgn;  35   !;   7   ?;  50   ^)
%                                         (  92   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

%------------------------------------------------------------------------------
%----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(a_type,type,(
a: mu )).

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

thf(con,conjecture,
( mvalid
@ ( mexists_ind
@ ^ [X: mu] :
( mbox_s4 @ ( qmltpeq @ X @ a ) ) ) )).

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