%------------------------------------------------------------------------------
% File     : LCL111-1 : TPTP v3.0.0. Released v1.0.0.
% Domain   : Logic Calculi (Many valued sentential)
% Problem  : MV-25 depends on the Merideth system
% Version  : [McC92] axioms.
% English  : An axiomatisation of the many valued sentential calculus 
%            is {MV-1,MV-2,MV-3,MV-5} by Meredith. Show that MV-25 depends 
%            on the Meredith system.

% Refs     : [Ove90] Overbeek (1990), ATP competition announced at CADE-10
%          : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio
%          : [McC92] McCune (1992), Email to G. Sutcliffe
%          : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal 
%          : [LM93]  Lusk & McCune (1993), Uniform Strategies: The CADE-11 
% Source   : [McC92]
% Names    : CADE-11 Competition 6 [Ove90]
%          : MV-57 [MW92]
%          : THEOREM 6 [LM93]
%          : mv.in part 2 [OTTER]
%          : mv25.in [OTTER]
%          : ovb6 [SETHEO]

% Status   : Unsatisfiable
% Rating   : 0.00 v2.4.0, 0.43 v2.3.0, 0.14 v2.2.1, 0.11 v2.2.0, 0.22 v2.1.0, 0.25 v2.0.0
% Syntax   : Number of clauses     :    6 (   0 non-Horn;   5 unit;   2 RR)
%            Number of atoms       :    8 (   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   :   11 (   1 singleton)
%            Maximal term depth    :    4 (   3 average)

% Comments : 
%          : tptp2X -f tptp:short LCL111-1.p 
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,(
    ~ is_a_theorem(implies(X,Y))
  | ~ is_a_theorem(X)
  | is_a_theorem(Y)   )).

cnf(mv_1,axiom,(
    is_a_theorem(implies(X,implies(Y,X)))   )).

cnf(mv_2,axiom,(
    is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))   )).

cnf(mv_3,axiom,(
    is_a_theorem(implies(implies(implies(X,Y),Y),implies(implies(Y,X),X)))   )).

cnf(mv_5,axiom,(
    is_a_theorem(implies(implies(not(X),not(Y)),implies(Y,X)))   )).

cnf(prove_mv_25,negated_conjecture,(
    ~ is_a_theorem(implies(implies(a,b),implies(implies(c,a),implies(c,b))))   )).
%------------------------------------------------------------------------------