TPTP Problem File: LCL542+1.p
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%------------------------------------------------------------------------------
% File : LCL542+1 : TPTP v8.2.0. Released v3.3.0.
% Domain : Logic Calculi (Propositional modal)
% Problem : Prove axiom m2 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 : 0.14 v8.1.0, 0.17 v7.5.0, 0.22 v7.4.0, 0.20 v7.3.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.20 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.30 v5.5.0, 0.33 v5.4.0, 0.32 v5.3.0, 0.44 v5.2.0, 0.35 v5.1.0, 0.38 v5.0.0, 0.33 v4.1.0, 0.30 v4.0.0, 0.29 v3.7.0, 0.25 v3.5.0, 0.26 v3.4.0, 0.37 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
% Comments :
%------------------------------------------------------------------------------
%----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_axiom_m2,conjecture,
axiom_m2 ).
%------------------------------------------------------------------------------