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GRP004-2.ax
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GRP004-2.ax
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%--------------------------------------------------------------------------
% File : GRP004-2 : TPTP v7.0.0. Bugfixed v1.2.0.
% Domain : Group Theory (Lattice Ordered)
% Axioms : Lattice ordered group (equality) axioms
% Version : [Fuc94] (equality) axioms.
% English :
% Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% Source : [Sch95]
% Names :
% Status : Satisfiable
% Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR)
% Number of atoms : 12 ( 12 equality)
% Maximal clause size : 1 ( 1 average)
% Number of predicates : 1 ( 0 propositional; 2-2 arity)
% Number of functors : 3 ( 0 constant; 2-2 arity)
% Number of variables : 28 ( 2 singleton)
% Maximal term depth : 3 ( 2 average)
% SPC :
% Comments : Requires GRP004-0.ax
%--------------------------------------------------------------------------
%----Specification of the least upper bound and greatest lower bound
cnf(symmetry_of_glb,axiom,
( greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) )).
cnf(symmetry_of_lub,axiom,
( least_upper_bound(X,Y) = least_upper_bound(Y,X) )).
cnf(associativity_of_glb,axiom,
( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) )).
cnf(associativity_of_lub,axiom,
( least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) )).
cnf(idempotence_of_lub,axiom,
( least_upper_bound(X,X) = X )).
cnf(idempotence_of_gld,axiom,
( greatest_lower_bound(X,X) = X )).
cnf(lub_absorbtion,axiom,
( least_upper_bound(X,greatest_lower_bound(X,Y)) = X )).
cnf(glb_absorbtion,axiom,
( greatest_lower_bound(X,least_upper_bound(X,Y)) = X )).
%----Monotony of multiply
cnf(monotony_lub1,axiom,
( multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) )).
cnf(monotony_glb1,axiom,
( multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) )).
cnf(monotony_lub2,axiom,
( multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) )).
cnf(monotony_glb2,axiom,
( multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)) )).
%--------------------------------------------------------------------------