TPTP Problem File: LCL603^1.p
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% File : LCL603^1 : TPTP v9.0.0. Released v3.6.0.
% Domain : Logical Calculi
% Problem : T and 4 imply reflexivity and transitivity of R in K
% Version : [BP09] axioms.
% English :
% Refs : [BP09] Benzmueller & Paulson (2009), Exploring Properties of
% Source : [BP09]
% Names : K-T4-b [BP09]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% Syntax : Number of formulae : 78 ( 36 unt; 41 typ; 36 def)
% Number of atoms : 98 ( 40 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 142 ( 6 ~; 3 |; 16 &; 106 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 224 ( 224 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 45 usr; 8 con; 0-4 aty)
% Number of variables : 110 ( 76 ^; 24 !; 10 ?; 110 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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%----Include simple maths definitions and axioms
include('Axioms/LCL008^0.ax').
include('Axioms/SET008^2.ax').
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%----Conjecture
thf(thm,conjecture,
! [R: $i > $i > $o] :
( ! [A: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ ( mbox @ R @ ( mbox @ R @ A ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ R @ A ) @ A ) ) )
=> ( ( reflexive @ R )
& ( transitive @ R ) ) ) ).
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