TPTP Problem File: NUM126-1.p
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%--------------------------------------------------------------------------
% File : NUM126-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain : Number Theory (Ordinals)
% Problem : Alternate 1 for transfinite induction, part 1
% Version : [Qua92] axioms.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : ORD18-5.1 [Quaife]
% Status : Unknown
% Rating : 1.00 v2.1.0
% Syntax : Number of clauses : 160 ( 48 unt; 12 nHn; 121 RR)
% Number of literals : 324 ( 72 equ; 157 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 : 63 ( 63 usr; 19 con; 0-3 aty)
% Number of variables : 303 ( 40 sgn)
% SPC : CNF_UNK_RFO_SEQ_NHN
% Comments : Not in [Qua92]. Theorem ORD18-5.1 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_alternate_1_transfinite_induction1_1,negated_conjecture,
~ member(least(element_relation,intersection(z,ordinal_numbers)),ordinal_numbers) ).
cnf(prove_alternate_1_transfinite_induction1_2,negated_conjecture,
intersection(z,ordinal_numbers) != null_class ).
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