TPTP Problem File: LCL109-6.p
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%--------------------------------------------------------------------------
% File : LCL109-6 : TPTP v9.0.0. Released v1.0.0.
% Domain : Logic Calculi (Wajsberg Algebra)
% Problem : A theorem in the lattice structure of Wajsberg algebras
% Version : [Bon91] (equality) axioms : Augmented.
% Theorem formulation : Alternative Wajsberg algebras lattice
% structure.
% English :
% Refs : [FRT84] Font et al. (1984), Wajsberg Algebras
% : [AB90] Anantharaman & Bonacina (1990), An Application of the
% : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic
% Source : [Bon91]
% Names : Lattice structure theorem 8 [Bon91]
% Status : Unsatisfiable
% Rating : 0.18 v8.2.0, 0.21 v8.1.0, 0.25 v7.5.0, 0.21 v7.4.0, 0.30 v7.3.0, 0.26 v7.1.0, 0.22 v7.0.0, 0.21 v6.4.0, 0.26 v6.3.0, 0.35 v6.2.0, 0.43 v6.1.0, 0.44 v6.0.0, 0.52 v5.5.0, 0.58 v5.4.0, 0.40 v5.3.0, 0.25 v5.2.0, 0.29 v5.1.0, 0.40 v5.0.0, 0.43 v4.1.0, 0.36 v4.0.0, 0.31 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 2 RR)
% Number of literals : 14 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 1 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
%--------------------------------------------------------------------------
%----Include Alternative Wajsberg algebra axioms
include('Axioms/LCL002-0.ax').
%--------------------------------------------------------------------------
%----Include some Alternative Wajsberg algebra definitions
% include('Axioms/LCL002-1.ax').
%----Definition that and_star is AC and xor is C
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ).
cnf(and_star_commutativity,axiom,
and_star(X,Y) = and_star(Y,X) ).
%----Definition of false in terms of true
cnf(false_definition,axiom,
not(truth) = falsehood ).
%----Include the definition of implies in terms of xor and and_star
cnf(implies_definition,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth ).
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