TPTP Problem File: LCL516+1.p
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%------------------------------------------------------------------------------
% File : LCL516+1 : TPTP v9.0.0. Released v3.3.0.
% Domain : Logic Calculi (Propositional)
% Problem : Prove Lukasiewicz's cn2 axiom from Rosser's axiomatization
% Version : [HB34] axioms.
% English :
% Refs : [HB34] Hilbert & Bernays (1934), Grundlagen der Mathematick
% : [Hal] Halleck (URL), John Halleck's Logic Systems
% Source : [TPTP]
% Names :
% Status : Theorem
% Rating : 0.55 v9.0.0, 0.56 v8.2.0, 0.58 v8.1.0, 0.53 v7.5.0, 0.59 v7.4.0, 0.63 v7.3.0, 0.69 v7.2.0, 0.72 v7.1.0, 0.78 v7.0.0, 0.60 v6.4.0, 0.73 v6.3.0, 0.71 v6.2.0, 0.72 v6.1.0, 0.80 v6.0.0, 0.74 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.85 v5.2.0, 0.75 v5.1.0, 0.71 v4.1.0, 0.70 v4.0.0, 0.71 v3.7.0, 0.70 v3.5.0, 0.68 v3.3.0
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 77 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 0 ~; 0 |; 1 &)
% ( 26 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 34 ( 33 usr; 32 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
%----Include axioms of propositional logic
include('Axioms/LCL006+0.ax').
include('Axioms/LCL006+1.ax').
%----Include Rosser's axiomatization of propositional logic
include('Axioms/LCL006+5.ax').
%------------------------------------------------------------------------------
%----Operator definitions to reduce everything to and & not
fof(luka_op_or,axiom,
op_or ).
fof(luka_op_implies,axiom,
op_implies ).
fof(luka_op_equiv,axiom,
op_equiv ).
fof(luka_cn2,conjecture,
cn2 ).
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