TPTP Problem File: ALG006-1.p
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%--------------------------------------------------------------------------
% File : ALG006-1 : TPTP v8.2.0. Released v2.2.0.
% Domain : General Algebra
% Problem : Simplification of Kalman's set difference basis (part 1)
% Version : [MP96] (equality) axioms : Especial.
% English : This is part 1 of a proof that one of the axioms in Kalman's
% basis for set difference can be simplified.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : SD-3-a [MP96]
% Status : Unsatisfiable
% Rating : 0.05 v8.2.0, 0.04 v8.1.0, 0.15 v7.5.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.06 v7.0.0, 0.05 v6.4.0, 0.11 v6.3.0, 0.06 v6.2.0, 0.06 v6.0.0, 0.24 v5.5.0, 0.26 v5.4.0, 0.07 v5.3.0, 0.00 v5.2.0, 0.07 v5.0.0, 0.00 v3.4.0, 0.12 v3.3.0, 0.00 v2.2.1
% Syntax : Number of clauses : 4 ( 4 unt; 0 nHn; 1 RR)
% Number of literals : 4 ( 4 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 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)) ).
%----Denial of simplified third axiom:
cnf(prove_set_difference_3_simplified,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c) ).
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