%--------------------------------------------------------------------------
% File     : LCL033-1 : TPTP v2.1.0. Released v1.0.0.
% Domain   : Logic Calculi (Implication/Falsehood 2 valued sentential)
% Problem  : C0-2 depends on the Merideth axiom
% Version  : [McC92] axioms.
% English  : Axiomatisations for the Implication/Falsehood 2 valued 
%            sentential calculus are {C0-1,C0-2,C0-3,C0-4} 
%            by Tarski-Bernays, {C0-2,C0-5,C0-6} by Church, and the single 
%            Meredith axioms. Show that C0-2 can be derived from the 
%            single Meredith 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    : C0-45 [MW92]

% Status   : unsatisfiable
% Rating   : 0.33 v2.1.0, 0.13 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 (   3 constant; 0-2 arity)
%            Number of variables  :    7 (   2 singleton)
%            Maximal term depth   :    6 (   2 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp LCL033-1.p 
%--------------------------------------------------------------------------
input_clause(condensed_detachment,axiom,
    [-- is_a_theorem(implies(X, Y)),
     -- is_a_theorem(X),
     ++ is_a_theorem(Y)]).

input_clause(c0_CAMerideth,axiom,
    [++ is_a_theorem(implies(implies(implies(implies(implies(X, Y), implies(Z, falsehood)), U), V), implies(implies(V, X), implies(Z, X))))]).

input_clause(prove_c0_2,conjecture,
    [-- is_a_theorem(implies(a, implies(b, a)))]).
%--------------------------------------------------------------------------