%--------------------------------------------------------------------------
% File     : LCL002-1 : TPTP v9.0.0. Released v1.0.0.
% Domain   : Logic Calculi (Disjunction/Negation 2 valued sentential)
% Problem  : AN-CAMerideth => AN-1
% Version  : [McC92] axioms.
% English  : The Whitehead-Russell axiomatisation of the Disjunction/
%            Negation 2 valued sentential calculus is {AN-1,AN-2,AN-3,
%            AN-4}. Show that AN-1 can be derived from the Merideth axiom.

% Refs     : [Mer53] Meredith (1953), Single Axioms for the Systems (C,N),
%          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : AN-51 [MW92]

% Status   : Unsatisfiable
% Rating   : 0.47 v9.0.0, 0.18 v8.2.0, 0.14 v8.1.0, 0.00 v7.4.0, 0.17 v7.3.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.64 v6.0.0, 0.44 v5.5.0, 0.62 v5.4.0, 0.61 v5.3.0, 0.70 v5.2.0, 0.62 v5.1.0, 0.69 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.1, 0.29 v3.4.0, 0.20 v3.3.0, 0.00 v3.2.0, 0.33 v3.1.0, 0.50 v2.7.0, 0.75 v2.6.0, 0.71 v2.4.0, 0.86 v2.3.0, 0.71 v2.2.1, 0.89 v2.1.0, 1.00 v2.0.0
% Syntax   : Number of clauses     :    3 (   2 unt;   0 nHn;   2 RR)
%            Number of literals    :    5 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 1-1 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :    7 (   1 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments :
%--------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
    ( ~ is_a_theorem(or(not(X),Y))
    | ~ is_a_theorem(X)
    | is_a_theorem(Y) ) ).

cnf(an_CAMerideth,axiom,
    is_a_theorem(or(not(or(not(or(not(X),Y)),or(Z,or(U,V)))),or(not(or(not(U),X)),or(Z,or(V,X))))) ).

cnf(an_1,negated_conjecture,
    ~ is_a_theorem(or(not(or(not(b),c)),or(not(or(a,b)),or(a,c)))) ).

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