TPTP Problem File: NUM228-1.p
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%--------------------------------------------------------------------------
% File : NUM228-1 : TPTP v8.2.0. Bugfixed v2.1.0.
% Domain : Number Theory (Ordinals)
% Problem : Corollary to recursion equation functions definition
% Version : [Qua92] axioms.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : TRECDEF4 cor. [Quaife]
% Status : Unsatisfiable
% Rating : 0.20 v8.2.0, 0.24 v8.1.0, 0.21 v7.4.0, 0.24 v7.3.0, 0.17 v7.0.0, 0.27 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.5.0, 0.20 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.21 v4.1.0, 0.31 v4.0.1, 0.36 v3.7.0, 0.40 v3.5.0, 0.36 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.08 v3.1.0, 0.18 v2.7.0, 0.17 v2.6.0, 0.00 v2.5.0, 0.09 v2.4.0, 0.00 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_UNS_RFO_SEQ_NHN
% Comments : Not in [Qua92]. Theorem TRECDEF4 cor. 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_corollary_1,negated_conjecture,
~ function(z) ).
cnf(prove_corollary_2,negated_conjecture,
recursion_equation_functions(z) != null_class ).
%--------------------------------------------------------------------------