TPTP Problem File: SET171-6.p
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%------------------------------------------------------------------------------
% File : SET171-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain : Set Theory
% Problem : Union distributes over intersection
% Version : [Qua92] axioms.
% English : The union of X and (the intersection of Y and Z) is the
% intersection of (the union of X and Y) and (the union of X and Z).
% 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 : D2.1 [Qua92]
% Status : Unsatisfiable
% Rating : 0.95 v8.2.0, 1.00 v2.1.0
% Syntax : Number of clauses : 113 ( 38 unt; 8 nHn; 80 RR)
% Number of literals : 219 ( 50 equ; 101 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 10 usr; 0 prp; 1-3 aty)
% Number of functors : 49 ( 49 usr; 15 con; 0-3 aty)
% Number of variables : 214 ( 32 sgn)
% 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).
% : Used as a demodulator by Quaife.
% 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_union_over_intersection1_1,negated_conjecture,
intersection(union(x,y),union(x,z)) != union(x,intersection(y,z)) ).
%------------------------------------------------------------------------------