TPTP Problem File: BOO038-1.p
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%--------------------------------------------------------------------------
% File : BOO038-1 : TPTP v8.2.0. Released v2.5.0.
% Domain : Boolean Algebra
% Problem : DN-1 is a single axiom for Boolean algebra
% Version : [EF+02] axioms.
% English : Show that equation DN-1 is a single axiom for Boolean algebra
% in terms of disjunction and negation by deriving the Huntington
% 3-basis.
% Refs : [EF+02] Ernst et al. (2002), More First-order Test Problems in
% : [MV+02] McCune et al. (2002), Short Single Axioms for Boolean
% Source : [EF+02]
% Names : ba-dn1 [EF+02]
% Status : Unsatisfiable
% Rating : 0.40 v8.2.0, 0.44 v8.1.0, 0.53 v7.5.0, 0.47 v7.4.0, 0.53 v7.3.0, 0.46 v7.2.0, 0.50 v7.1.0, 0.36 v7.0.0, 0.46 v6.4.0, 0.57 v6.3.0, 0.50 v6.2.0, 0.60 v6.1.0, 0.55 v6.0.0, 0.29 v5.5.0, 0.38 v5.4.0, 0.56 v5.3.0, 0.60 v5.2.0, 0.38 v5.1.0, 0.33 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.38 v4.0.0, 0.29 v3.4.0, 0.33 v3.2.0, 0.22 v3.1.0, 0.20 v2.7.0, 0.38 v2.6.0, 0.40 v2.5.0
% Syntax : Number of clauses : 2 ( 1 unt; 0 nHn; 1 RR)
% Number of literals : 4 ( 4 equ; 3 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 2 sgn)
% SPC : CNF_UNS_RFO_PEQ_NUE
% Comments :
%--------------------------------------------------------------------------
%----DN-1
cnf(dn1,axiom,
inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C ).
%----Denial of Huntington 3-basis
cnf(huntinton,negated_conjecture,
( add(b,a) != add(a,b)
| add(add(a,b),c) != add(a,add(b,c))
| add(inverse(add(inverse(a),b)),inverse(add(inverse(a),inverse(b)))) != a ) ).
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