TPTP Problem File: LCL690^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : LCL690^1 : TPTP v9.0.0. Released v3.7.0.
% Domain : Logical Calculi
% Problem : Prove K in the CS4 translation
% Version : [AM+01] axioms.
% English :
% Refs : [AM+01] Alechina et al. (2001), Categorical and Kripke Semanti
% : [Gar09] Garg (2009), Email to Geoff Sutcliffe
% Source : [Gar09]
% Names :
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.44 v7.3.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.1.0, 0.80 v5.0.0, 0.60 v4.1.0, 0.67 v3.7.0
% Syntax : Number of formulae : 61 ( 24 unt; 31 typ; 24 def)
% Number of atoms : 117 ( 24 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 106 ( 3 ~; 1 |; 2 &; 99 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 7 con; 0-3 aty)
% Number of variables : 53 ( 38 ^; 11 !; 4 ?; 53 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
%------------------------------------------------------------------------------
%----Include axioms of multi-modal logic
include('Axioms/LCL008^0.ax').
%----Include axioms translating constructive S4 (CS4) to bimodal classical
%----S4 (BS4)
include('Axioms/LCL009^0.ax').
%------------------------------------------------------------------------------
thf(cs4_k,conjecture,
! [A: $i > $o,B: $i > $o] : ( cs4_valid @ ( cs4_impl @ ( cs4_box @ ( cs4_impl @ ( cs4_atom @ A ) @ ( cs4_atom @ B ) ) ) @ ( cs4_impl @ ( cs4_box @ ( cs4_atom @ A ) ) @ ( cs4_box @ ( cs4_atom @ B ) ) ) ) ) ).
%------------------------------------------------------------------------------