%------------------------------------------------------------------------------
% File     : SYO489^6 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Syntactic
% Problem  : Ted Sider's S5 quantified modal logic wff 15
% Version  : Especial.
% English  :

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

% Status   : CounterSatisfiable
% Rating   : 0.33 v9.0.0, 0.25 v8.2.0, 0.50 v8.1.0, 0.60 v7.5.0, 0.40 v7.4.0, 0.50 v7.2.0, 0.33 v6.2.0, 0.00 v5.4.0, 0.67 v5.0.0, 0.33 v4.1.0, 0.50 v4.0.0
% Syntax   : Number of formulae    :   75 (  33 unt;  38 typ;  33 def)
%            Number of atoms       :  117 (  38 equ;   0 cnn)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  148 (   5   ~;   5   |;   8   &; 122   @)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   1 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  182 ( 182   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   43 (  41 usr;   6 con; 0-3 aty)
%            Number of variables   :   88 (  52   ^;  30   !;   6   ?;  88   :)
% 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(f_type,type,
    f: mu > $i > $o ).

thf(g_type,type,
    g: mu > $i > $o ).

thf(prove,conjecture,
    mvalid @ ( mimplies @ ( mand @ ( mdia_s5 @ ( f @ a ) ) @ ( mdia_s5 @ ( g @ a ) ) ) @ ( mdia_s5 @ ( mand @ ( f @ a ) @ ( g @ a ) ) ) ) ).

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