%--------------------------------------------------------------------------
% File     : LCL051-1 : TPTP v2.1.0. Released v1.0.0.
% Domain   : Logic Calculi (Implication/Negation 2 valued sentential)
% Problem  : CN-22 depends on the Lukasiewicz system
% 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-22 depends on the short Lukasiewicz system.

% Refs     : [LM92]  Lusk & McCune (1992), Experiments with ROO, a Parallel
%          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
% Source   : [McC92]
% Names    : CD-12 [LM92]
%          : CN-12 [MW92]

% Status   : unsatisfiable
% Rating   : 0.78 v2.1.0, 0.88 v2.0.0
% Syntax   : Number of clauses    :    5 (   0 non-Horn;   4 unit;   2 RR)
%            Number of literals   :    7 (   0 equality)
%            Maximal clause size  :    3 (   1 average)
%            Number of predicates :    1 (   0 propositional; 1-1 arity)
%            Number of functors   :    5 (   3 constant; 0-2 arity)
%            Number of variables  :    8 (   1 singleton)
%            Maximal term depth   :    4 (   2 average)

% Comments : 
%          : tptp2X -f tptp -t rm_equality:rstfp LCL051-1.p 
%--------------------------------------------------------------------------
input_clause(condensed_detachment,axiom,
    [-- is_a_theorem(implies(X, Y)),
     -- is_a_theorem(X),
     ++ is_a_theorem(Y)]).

input_clause(cn_1,axiom,
    [++ is_a_theorem(implies(implies(X, Y), implies(implies(Y, Z), implies(X, Z))))]).

input_clause(cn_2,axiom,
    [++ is_a_theorem(implies(implies(not(X), X), X))]).

input_clause(cn_3,axiom,
    [++ is_a_theorem(implies(X, implies(not(X), Y)))]).

input_clause(prove_cn_22,conjecture,
    [-- is_a_theorem(implies(implies(b, c), implies(implies(a, b), implies(a, c))))]).
%--------------------------------------------------------------------------