%--------------------------------------------------------------------------
% File     : LCL131-1 : TPTP v2.1.0. Released v1.0.0.
% Domain   : Logic Calculi (Right group)
% Problem  : LG-2 depends on S-6
% Version  : [McC92b] axioms.
% English  : Kalman's axiomatisation of the right group calculus 
%            is {LG-1,LG-2,LG-3,LG-4,LG-5}. McCune has shown that LG-2 
%            is a single axiom. Other axiomatisations by McCune are 
%            {Q-2,Q-3}, {Q-3,Q-4}, S-2, S-3, S-4, P-4, S-6. Show that LG-2 
%            depends on S-6.

% Refs     : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92a] McCune (1992), Automated Discovery of New Axiomatisat
%          : [McC92b] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92b]
% Names    : RG-112 [MW92]

% Status   : unsatisfiable
% Rating   : 0.67 v2.1.0, 0.75 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   :    5 (   4 constant; 0-2 arity)
%            Number of variables  :    6 (   0 singleton)
%            Maximal term depth   :    6 (   3 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp LCL131-1.p 
%--------------------------------------------------------------------------
input_clause(condensed_detachment,axiom,
    [-- is_a_theorem(equivalent(X, Y)),
     -- is_a_theorem(X),
     ++ is_a_theorem(Y)]).

input_clause(s_6,axiom,
    [++ is_a_theorem(equivalent(equivalent(X, equivalent(equivalent(equivalent(Y, Z), equivalent(U, Z)), equivalent(Y, U))), X))]).

input_clause(prove_lg_2,conjecture,
    [-- is_a_theorem(equivalent(a, equivalent(a, equivalent(equivalent(b, c), equivalent(equivalent(b, e), equivalent(c, e))))))]).
%--------------------------------------------------------------------------