TPTP Problem File: LCL621^1.p
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% File : LCL621^1 : TPTP v8.2.0. Released v3.6.0.
% Domain : Logical Calculi
% Problem : A simple theorem of K4
% Version : [Ben08] axioms.
% English :
% Refs : [Fit07] Fitting (2007), Modal Proof Theory
% : [Ben08] Benzmueller (2008), Email to G. Sutcliffe
% Source : [Ben08]
% Names : Fitting-HB-10 [Ben08]
% Status : Theorem
% Rating : 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% Syntax : Number of formulae : 37 ( 15 unt; 20 typ; 15 def)
% Number of atoms : 51 ( 15 equ; 0 cnn)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 61 ( 3 ~; 1 |; 2 &; 54 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 8 con; 0-3 aty)
% Number of variables : 41 ( 28 ^; 9 !; 4 ?; 41 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include simple maths definitions and axioms
include('Axioms/LCL008^0.ax').
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%----Axioms
thf(k4,axiom,
! [R: $i > $i > $o,X: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ R @ X ) @ ( mbox @ R @ ( mbox @ R @ X ) ) ) ) ).
%----Conjecture
thf(thm,conjecture,
! [R: $i > $i > $o,X: $i > $o,Y: $i > $o] : ( mvalid @ ( mimpl @ ( mand @ ( mbox @ R @ ( mdia @ R @ X ) ) @ ( mbox @ R @ Y ) ) @ ( mbox @ R @ ( mdia @ R @ ( mand @ X @ Y ) ) ) ) ) ).
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