TPTP Problem File: SYO490^6.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SYO490^6 : TPTP v9.0.0. 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 v9.0.0, 0.75 v8.2.0, 1.00 v8.1.0, 0.80 v7.5.0, 0.60 v7.4.0, 0.75 v7.2.0, 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 ( 33 unt; 37 typ; 33 def)
% Number of atoms : 116 ( 38 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 147 ( 5 ~; 5 |; 8 &; 121 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 181 ( 181 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 7 con; 0-3 aty)
% Number of variables : 91 ( 55 ^; 30 !; 6 ?; 91 :)
% SPC : TH0_CSA_EQU_NAR
% Comments :
%------------------------------------------------------------------------------
%----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 ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------