%--------------------------------------------------------------------------
% File     : LCL068-1 : TPTP v9.0.0. Bugfixed v1.2.0.
% Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
% Problem  : CN-2 depends on the second Lukasiewicz system
% Version  : [McC92] axioms.
% English  : Axiomatisations of the Implication/Negation 2 valued
%            sentential calculus are {CN-1,CN-2,CN-3} by Lukasiewicz,
%            {CN-18,CN-21,CN-35,CN-39,CN-39,CN-40,CN-46} by Frege,
%            {CN-3,CN-18,CN-21,CN-22,CN-30,CN-54} by Hilbert, {CN-18,
%            CN-35,CN-49} by Church, {CN-19,CN-37,CN-59} by Lukasiewicz,
%            {CN-19,CN-37,CN-60} by Wos, and the single Meredith axiom.
%            Show that CN-2 depends on the second Lukasiewicz system.

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : CN-29 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.00 v6.1.0, 0.29 v6.0.0, 0.00 v5.5.0, 0.25 v5.4.0, 0.33 v5.3.0, 0.40 v5.2.0, 0.23 v5.1.0, 0.31 v5.0.0, 0.27 v4.1.0, 0.33 v4.0.1, 0.14 v3.4.0, 0.00 v3.1.0, 0.17 v2.7.0, 0.25 v2.6.0, 0.29 v2.5.0, 0.00 v2.4.0, 0.00 v2.3.0, 0.14 v2.2.1, 0.67 v2.1.0, 0.67 v2.0.0
% Syntax   : Number of clauses     :    5 (   4 unt;   0 nHn;   2 RR)
%            Number of literals    :    7 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-2 aty)
%            Number of variables   :   11 (   2 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments :
% Bugfixes : v1.2.0 - Clause prove_cn_2 fixed.
%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
    ( ~ is_a_theorem(implies(X,Y))
    | ~ is_a_theorem(X)
    | is_a_theorem(Y) ) ).

cnf(cn_19,axiom,
    is_a_theorem(implies(implies(implies(X,Y),Z),implies(Y,Z))) ).

cnf(cn_37,axiom,
    is_a_theorem(implies(implies(implies(X,Y),Z),implies(not(X),Z))) ).

cnf(cn_59,axiom,
    is_a_theorem(implies(implies(not(X),Z),implies(implies(Y,Z),implies(implies(X,Y),Z)))) ).

cnf(prove_cn_2,negated_conjecture,
    ~ is_a_theorem(implies(implies(not(a),a),a)) ).

%--------------------------------------------------------------------------