TPTP Problem File: ROB020-1.p
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%--------------------------------------------------------------------------
% File : ROB020-1 : TPTP v8.2.0. Released v1.0.0.
% Domain : Robbins Algebra
% Problem : -(a + -b)=b => Boolean
% Version : [Win90] (equality) axioms.
% Theorem formulation : Denies Huntington's axiom.
% English : If there exist a, b such that -(a + -b) = b, the algebra
% is Boolean.
% Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras
% : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% Source : [Win90]
% Names : Corollary 3.10 [Win90]
% Status : Unknown
% Rating : 1.00 v2.0.0
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 2 RR)
% Number of literals : 5 ( 5 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% SPC : CNF_UNK_RFO_PEQ_UEQ
% Comments : Commutativity, associativity, and Huntington's axiom
% axiomatize Boolean algebra.
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
%--------------------------------------------------------------------------
cnf(condition1,hypothesis,
negate(add(a,negate(b))) = b ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
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