## TPTP Problem File: LCL617^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : LCL617^1 : TPTP v7.0.0. Released v3.6.0.
% Domain   : Logical Calculi
% Problem  : Axiom GL - the Loeb formula
% Version  : [Ben08] axioms.
% English  :

% Refs     : [Fit07] Fitting (2007), Modal Proof Theory
%          : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% Source   : [Ben08]
% Names    : Fitting-HB-7a [Ben08]

% Status   : CounterSatisfiable
% Rating   : 0.33 v6.4.0, 0.67 v6.3.0, 0.33 v4.1.0, 0.00 v4.0.0, 1.00 v3.7.0
% Syntax   : Number of formulae    :   36 (   0 unit;  20 type;  15 defn)
%            Number of atoms       :   89 (  15 equality;  46 variable)
%            Maximal formula depth :   11 (   5 average)
%            Number of connectives :   46 (   3   ~;   1   |;   2   &;  39   @)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   82 (  82   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   25 (  20   :;   0   =)
%            Number of variables   :   38 (   2 sgn;   6   !;   4   ?;  28   ^)
%                                         (  38   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_CSA_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
%----Include simple maths definitions and axioms
include('Axioms/LCL008^0.ax').
%------------------------------------------------------------------------------
%----Conjecture
thf(thm,conjecture,(
! [R: \$i > \$i > \$o,X: \$i > \$o] :
( mvalid @ ( mimpl @ ( mbox @ R @ ( mimpl @ ( mbox @ R @ X ) @ X ) ) @ ( mbox @ R @ X ) ) ) )).

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