%--------------------------------------------------------------------------
% File     : LCL075-1 : TPTP v2.1.0. Released v1.0.0.
% Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
% Problem  : CN-3 depends on the single Merideth axiom
% 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-3 depends on the single Meredith axiom.

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : CN-36 [MW92]

% Status   : unsatisfiable
% Rating   : 0.56 v2.1.0, 0.38 v2.0.0
% Syntax   : Number of clauses    :    3 (   0 non-Horn;   2 unit;   2 RR)
%            Number of literals   :    5 (   0 equality)
%            Maximal clause size  :    3 (   1 average)
%            Number of predicates :    1 (   0 propositional; 1-1 arity)
%            Number of functors   :    4 (   2 constant; 0-2 arity)
%            Number of variables  :    7 (   1 singleton)
%            Maximal term depth   :    7 (   3 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp LCL075-1.p 
%--------------------------------------------------------------------------
input_clause(condensed_detachment,axiom,
    [-- is_a_theorem(implies(X, Y)),
     -- is_a_theorem(X),
     ++ is_a_theorem(Y)]).

input_clause(cn_CAMerideth,axiom,
    [++ is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(not(Z), not(U))), Z), V), implies(implies(V, X), implies(U, X))))]).

input_clause(prove_cn_3,conjecture,
    [-- is_a_theorem(implies(a, implies(not(a), b)))]).
%--------------------------------------------------------------------------