## TPTP Problem File: SYO567^7.p

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%------------------------------------------------------------------------------
% File     : SYO567^7 : TPTP v7.2.0. Released v5.5.0.
% Domain   : Syntactic
% Problem  : Girle problem
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Gir00] Girle (2000), Modal Logics and Philosophy
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-SYM013+1 [Ben12]

% Status   : CounterSatisfiable
% Rating   : 0.50 v7.2.0, 0.33 v5.5.0
% Syntax   : Number of formulae    :   75 (   0 unit;  38 type;  32 defn)
%            Number of atoms       :  266 (  36 equality; 147 variable)
%            Maximal formula depth :   11 (   6 average)
%            Number of connectives :  162 (   5   ~;   5   |;   9   &; 133   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  184 ( 184   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   42 (  38   :;   0   =)
%            Number of variables   :   93 (   2 sgn;  34   !;   7   ?;  52   ^)
%                                         (  93   :;   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(g_type,type,(
g: mu > \$i > \$o )).

thf(f_type,type,(
f: mu > \$i > \$o )).

thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X: mu] :
( mimplies @ ( f @ X ) @ ( mbox_s4 @ ( g @ X ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X: mu] :
( f @ X ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( g @ X ) ) ) ) ) )).

%------------------------------------------------------------------------------