## TPTP Problem File: SYO490^6.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SYO490^6 : TPTP v7.1.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : Ted Sider's S5 quantified modal logic wff 16
% Version  : Especial.
% English  :

% Refs     : [Sid09] Sider (2009), Logic for Philosophy
% Source   : [Sid09]
% Names    :

% Status   : CounterSatisfiable
% Rating   : 0.67 v6.2.0, 0.33 v5.4.0, 1.00 v5.0.0, 0.67 v4.1.0, 0.50 v4.0.0
% Syntax   : Number of formulae    :   74 (   0 unit;  37 type;  33 defn)
%            Number of atoms       :  255 (  38 equality; 138 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  147 (   5   ~;   5   |;   8   &; 121   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  181 ( 181   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  37   :;   0   =)
%            Number of variables   :   91 (   3 sgn;  30   !;   6   ?;  55   ^)
%                                         (  91   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

%------------------------------------------------------------------------------
%----Include axioms for modal logic S5
include('Axioms/LCL013^0.ax').
include('Axioms/LCL013^6.ax').
%------------------------------------------------------------------------------
thf(a_type,type,(
a: mu )).

thf(r_type,type,(
r: mu > mu > \$i > \$o )).

thf(prove,conjecture,
( mvalid
@ ( mimplies
@ ( mexists_ind
@ ^ [X: mu] :
( mdia_s5 @ ( r @ a @ X ) ) )
@ ( mdia_s5
@ ( mbox_s5
@ ( mexists_ind
@ ^ [X: mu] :
( mexists_ind
@ ^ [Y: mu] :
( r @ X @ Y ) ) ) ) ) ) )).

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