TPTP Problem File: LAT011-1.p
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%--------------------------------------------------------------------------
% File : LAT011-1 : TPTP v8.2.0. Released v2.2.0.
% Domain : Lattice Theory
% Problem : Uniqueness of meet (dually join) in lattice theory
% Version : [MP96] (equality) axioms : Especial.
% English : Let's say we have a lattice with two meet operations, say
% meet1 and meet2. In other words, {join,meet1} is a lattice,
% and {join,meet2} is a lattice. Then, we can prove that the
% two meet operations are really the same.
% Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% Source : [McC98]
% Names : LT-8 [MP96]
% Status : Unsatisfiable
% Rating : 0.09 v8.2.0, 0.12 v8.1.0, 0.05 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.3.0, 0.06 v6.2.0, 0.14 v6.1.0, 0.25 v6.0.0, 0.38 v5.5.0, 0.42 v5.4.0, 0.27 v5.3.0, 0.17 v5.2.0, 0.21 v5.1.0, 0.20 v5.0.0, 0.14 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.08 v3.7.0, 0.00 v3.3.0, 0.07 v3.1.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 1 RR)
% Number of literals : 14 ( 14 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 4 sgn)
% SPC : CNF_UNS_RFO_PEQ_UEQ
% Comments : For quasilattice, meet (dually join) is not necessarily unique.
%--------------------------------------------------------------------------
%----Include lattice axioms
include('Axioms/LAT001-0.ax').
%--------------------------------------------------------------------------
%----{join,meet2} is a lattice:
cnf(idempotence_of_meet2,axiom,
meet2(X,X) = X ).
cnf(commutativity_of_meet2,axiom,
meet2(X,Y) = meet2(Y,X) ).
cnf(absorption1_2,axiom,
meet2(X,join(X,Y)) = X ).
cnf(absorption2_2,axiom,
join(X,meet2(X,Y)) = X ).
cnf(associativity_of_meet2,axiom,
meet2(meet2(X,Y),Z) = meet2(X,meet2(Y,Z)) ).
%----Denial that meet1 and meet2 are the same:
cnf(prove_meets_are_same,negated_conjecture,
meet(a,b) != meet2(a,b) ).
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