TPTP Problem File: NUM181-1.p
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%--------------------------------------------------------------------------
% File : NUM181-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain : Number Theory (Ordinals)
% Problem : The null class is not a limit ordinal
% Version : [Qua92] axioms.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : LIM2.2 [Quaife]
% Status : Unsatisfiable
% Rating : 0.20 v8.2.0, 0.24 v8.1.0, 0.26 v7.5.0, 0.32 v7.4.0, 0.29 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.33 v6.3.0, 0.36 v6.2.0, 0.40 v6.1.0, 0.50 v6.0.0, 0.60 v5.5.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.76 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, 0.67 v3.3.0, 0.64 v3.2.0, 0.62 v3.1.0, 0.64 v2.7.0, 0.75 v2.6.0, 0.67 v2.5.0, 0.64 v2.4.0, 0.50 v2.3.0, 0.62 v2.2.1, 1.00 v2.1.0
% Syntax : Number of clauses : 159 ( 47 unt; 12 nHn; 120 RR)
% Number of literals : 323 ( 71 equ; 155 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 0 prp; 1-3 aty)
% Number of functors : 62 ( 62 usr; 18 con; 0-3 aty)
% Number of variables : 303 ( 40 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : Not in [Qua92]. Theorem LIM2.2 in [Quaife].
% : Quaife proves all these problems by augmenting the axioms with
% all previously proved theorems. The user may create an augmented
% version of this problem by adding all previously proved theorems.
% These include all of [Qua92]'s set theory and Boolean algebra
% theorems, available from the SET domain.
% 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 Set theory (Boolean algebra) axioms based on NBG set theory
include('Axioms/SET004-1.ax').
%----Include ordinal number theory axioms.
include('Axioms/NUM004-0.ax').
%--------------------------------------------------------------------------
cnf(prove_null_class_is_not_a_limit_ordinal_1,negated_conjecture,
member(null_class,limit_ordinals) ).
%--------------------------------------------------------------------------