TPTP Problem File: NUM009-1.p
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%--------------------------------------------------------------------------
% File : NUM009-1 : TPTP v9.0.0. Bugfixed v1.2.1.
% Domain : Number Theory
% Problem : Peano axiom 1
% Version : [BL+86] axioms.
% English :
% Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source : [BL+86]
% Names : Problem 233 [BL+86]
% Status : Unsatisfiable
% Rating : 0.05 v9.0.0, 0.10 v8.1.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.13 v6.4.0, 0.07 v6.3.0, 0.09 v6.2.0, 0.00 v5.5.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.12 v5.1.0, 0.18 v5.0.0, 0.14 v4.1.0, 0.15 v4.0.1, 0.09 v4.0.0, 0.00 v3.4.0, 0.08 v3.3.0, 0.14 v3.2.0, 0.15 v3.1.0, 0.09 v2.7.0, 0.08 v2.6.0, 0.00 v2.5.0, 0.18 v2.4.0, 0.12 v2.2.1, 0.00 v2.1.0, 0.25 v2.0.0
% Syntax : Number of clauses : 220 ( 12 unt; 59 nHn; 190 RR)
% Number of literals : 637 ( 75 equ; 349 neg)
% Maximal clause size : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 0 prp; 1-5 aty)
% Number of functors : 91 ( 91 usr; 12 con; 0-5 aty)
% Number of variables : 484 ( 32 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
% Bugfixes : v1.2.1 - Bugfix in NUM003-0.ax.
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%----Include Godel's set axioms
include('Axioms/SET003-0.ax').
%----Include the axioms for algebra from Godel's set axioms
include('Axioms/ALG001-0.ax').
%----Include the axioms for number theory from Godel's set axioms
include('Axioms/NUM003-0.ax').
%--------------------------------------------------------------------------
cnf(prove_zero_is_a_natural,negated_conjecture,
~ member(empty_set,natural_numbers) ).
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