%--------------------------------------------------------------------------
% File     : LCL009-1 : TPTP v2.1.0. Released v1.0.0.
% Domain   : Logic Calculi (Equivalential)
% Problem  : EC-5 depends on YQL
% Version  : [McC92] axioms.
% English  : An axiomatisation of the equivalential calculus is {EC-4, 
%            EC-5} by Wajsburg. Show that EC-5 can be derived from the 
%            single Lukasiewicz axiom YQL.

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : EC-72 [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  :    5 (   0 singleton)
%            Maximal term depth   :    4 (   2 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp LCL009-1.p 
%--------------------------------------------------------------------------
input_clause(condensed_detachment,axiom,
    [-- is_a_theorem(equivalent(X, Y)),
     -- is_a_theorem(X),
     ++ is_a_theorem(Y)]).

input_clause(yql,axiom,
    [++ is_a_theorem(equivalent(equivalent(X, Y), equivalent(equivalent(Z, Y), equivalent(X, Z))))]).

input_clause(prove_ec_5,conjecture,
    [-- is_a_theorem(equivalent(equivalent(equivalent(a, b), c), equivalent(a, equivalent(b, c))))]).
%--------------------------------------------------------------------------