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%--------------------------------------------------------------------------
% File : SET183-6 : TPTP v6.4.0. Bugfixed v2.1.0.
% Domain : Set Theory
% Problem : If X is a subset of Y, then the intersection of X and Y is X
% Version : [Qua92] axioms.
% English :
% Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : SU1 [Qua92]
% Status : Unsatisfiable
% Rating : 0.47 v6.3.0, 0.45 v6.2.0, 0.50 v6.1.0, 0.64 v6.0.0, 0.70 v5.5.0, 0.85 v5.3.0, 0.89 v5.2.0, 0.81 v5.1.0, 0.82 v5.0.0, 0.79 v4.1.0, 0.77 v4.0.1, 0.73 v3.7.0, 0.60 v3.5.0, 0.64 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0, 0.69 v3.1.0, 0.45 v2.7.0, 0.50 v2.6.0, 0.56 v2.5.0, 0.64 v2.4.0, 0.62 v2.2.1, 0.83 v2.2.0, 0.67 v2.1.0
% Syntax : Number of clauses : 114 ( 8 non-Horn; 39 unit; 81 RR)
% Number of atoms : 220 ( 50 equality)
% Maximal clause size : 5 ( 2 average)
% Number of predicates : 11 ( 0 propositional; 1-3 arity)
% Number of functors : 48 ( 14 constant; 0-3 arity)
% Number of variables : 214 ( 32 singleton)
% Maximal term depth : 6 ( 2 average)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : Quaife proves all these problems by augmenting the axioms with
% all previously proved theorems. With a few exceptions (the
% problems that correspond to [BL+86] problems), the TPTP has
% retained the order in which Quaife presents the problems. The
% user may create an augmented version of this problem by adding
% all previously proved theorems (the ones that correspond to
% [BL+86] are easily identified and positioned using Quaife's
% naming scheme).
% Bugfixes : v1.0.1 - Bugfix in SET004-1.ax.
% : v2.1.0 - Bugfix in SET004-0.ax.
%--------------------------------------------------------------------------
%----Include von Neuman-Bernays-Godel set theory axioms
include('Axioms/SET004-0.ax').
%----Include von Neuman-Bernays-Godel Boolean Algebra definitions
include('Axioms/SET004-1.ax').
%--------------------------------------------------------------------------
cnf(prove_subclass_property1_1,negated_conjecture,
( subclass(x,y) )).
cnf(prove_subclass_property1_2,negated_conjecture,
( intersection(x,y) != x )).
%--------------------------------------------------------------------------
|
