## TPTP Problem File: LCL538+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : LCL538+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Logic Calculi (Propositional modal)
% Problem  : Prove strict implies modus ponens from KM4B axiomatization of S5
% Version  : [HC96] axioms.
% English  :

% Refs     : [HC96]  Hughes & Cresswell (1996), A New Introduction to Modal
%          : [Hal]   Halleck (URL), John Halleck's Logic Systems
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.19 v8.2.0, 0.17 v8.1.0, 0.19 v7.5.0, 0.25 v7.4.0, 0.23 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.31 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.37 v6.0.0, 0.35 v5.5.0, 0.33 v5.4.0, 0.36 v5.3.0, 0.44 v5.2.0, 0.35 v5.1.0, 0.38 v4.1.0, 0.39 v4.0.1, 0.43 v4.0.0, 0.42 v3.7.0, 0.35 v3.5.0, 0.37 v3.4.0, 0.26 v3.3.0
% Syntax   : Number of formulae    :   89 (  31 unt;   0 def)
%            Number of atoms       :  156 (  11 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   67 (   0   ~;   0   |;   3   &)
%                                         (  49 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   61 (  60 usr;  59 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   0 con; 1-2 aty)
%            Number of variables   :  110 ( 110   !;   0   ?)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
%----Include Hilbert's axiomatization of propositional logic
include('Axioms/LCL006+0.ax').
include('Axioms/LCL006+1.ax').
include('Axioms/LCL006+2.ax').
%----Include axioms of modal logic
include('Axioms/LCL007+0.ax').
include('Axioms/LCL007+1.ax').
%----Include axioms for KM4B
include('Axioms/LCL007+3.ax').
%------------------------------------------------------------------------------
%----Modal definitions
fof(s1_0_op_possibly,axiom,
op_possibly ).

fof(s1_0_op_or,axiom,
op_or ).

fof(s1_0_op_implies,axiom,
op_implies ).

fof(s1_0_op_strict_implies,axiom,
op_strict_implies ).

fof(s1_0_op_equiv,axiom,
op_equiv ).

fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv ).

%----Conjecture
fof(s1_0_modus_ponens_strict_implies,conjecture,
modus_ponens_strict_implies ).

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