TPTP Problem File: ALG005-1.p
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%--------------------------------------------------------------------------
% File : ALG005-1 : TPTP v9.0.0. Released v2.2.0.
% Domain : General Algebra
% Problem : Associativity of intersection in terms of set difference.
% Version : [MP96] (equality) axioms : Especial.
% English : Starting with Kalman's basis for families of sets closed under
% set difference, we define intersection and show it to be
% associative.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : SD-2-a [MP96]
% Status : Unsatisfiable
% Rating : 0.09 v8.2.0, 0.17 v8.1.0, 0.20 v7.5.0, 0.25 v7.4.0, 0.26 v7.3.0, 0.11 v7.0.0, 0.16 v6.4.0, 0.21 v6.3.0, 0.18 v6.2.0, 0.25 v6.0.0, 0.43 v5.5.0, 0.42 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.27 v5.0.0, 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, 0.22 v2.7.0, 0.00 v2.2.1
% 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 : 3 ( 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 : 9 ( 1 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments :
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%----Kalman's axioms for set difference:
cnf(set_difference_1,axiom,
difference(X,difference(Y,X)) = X ).
cnf(set_difference_2,axiom,
difference(X,difference(X,Y)) = difference(Y,difference(Y,X)) ).
cnf(set_difference_3,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)) ).
%----Definition of intersection:
cnf(intersection,axiom,
multiply(X,Y) = difference(X,difference(X,Y)) ).
%----Denial of associativity:
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)) ).
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