TPTP Problem File: ROB023-1.p
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%--------------------------------------------------------------------------
% File : ROB023-1 : TPTP v9.0.0. Released v1.0.0.
% Domain : Robbins Algebra
% Problem : X + X=X => Boolean
% Version : [Win90] (equality) axioms.
% English : If for all X X + X = X then the algebra is Boolean.
% Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras
% : [Win90] Winker (1990), Robbins Algebra: Conditions that make a
% : [LM92] Lusk & McCune (1992), Experiments with ROO, a Parallel
% : [McC92] McCune (1992), Email to G. Sutcliffe
% Source : [McC92]
% Names : Robbins [LM92]
% Status : Unsatisfiable
% Rating : 0.18 v9.0.0, 0.14 v8.2.0, 0.21 v8.1.0, 0.30 v7.5.0, 0.21 v7.4.0, 0.26 v7.3.0, 0.21 v7.1.0, 0.11 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.24 v6.2.0, 0.21 v6.1.0, 0.19 v6.0.0, 0.38 v5.5.0, 0.32 v5.4.0, 0.13 v5.3.0, 0.08 v5.2.0, 0.14 v5.1.0, 0.13 v5.0.0, 0.14 v4.1.0, 0.09 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.43 v2.1.0, 0.38 v2.0.0
% Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 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 : 8 ( 0 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : Commutativity, associativity, and Huntington's axiom
% axiomatize Boolean algebra.
%--------------------------------------------------------------------------
%----Include axioms for Robbins algebra
include('Axioms/ROB001-0.ax').
%--------------------------------------------------------------------------
cnf(x_plus_x_is_x,hypothesis,
add(X,X) = X ).
cnf(prove_huntingtons_axiom,negated_conjecture,
add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))) != b ).
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