%--------------------------------------------------------------------------
% File     : NUM094-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain   : Number Theory (Ordinals)
% Problem  : Sections property 3
% Version  : [Qua92] axioms.
% English  :

% Refs     : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source   : [Quaife]
% Names    : SE3.1 [Quaife]

% Status   : Unsatisfiable
% Rating   : 0.70 v9.0.0, 0.75 v8.2.0, 0.71 v8.1.0, 0.58 v7.4.0, 0.65 v7.3.0, 0.58 v7.1.0, 0.50 v7.0.0, 0.53 v6.3.0, 0.55 v6.2.0, 0.50 v6.1.0, 0.79 v6.0.0, 0.70 v5.5.0, 0.85 v5.4.0, 0.90 v5.3.0, 0.94 v5.2.0, 0.88 v5.0.0, 0.86 v4.1.0, 0.77 v4.0.1, 0.82 v3.7.0, 0.70 v3.5.0, 0.73 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0, 0.77 v3.1.0, 0.73 v2.7.0, 0.83 v2.6.0, 0.78 v2.5.0, 0.91 v2.4.0, 0.88 v2.2.1, 0.83 v2.2.0, 0.67 v2.1.0
% Syntax   : Number of clauses     :  162 (  50 unt;  12 nHn; 123 RR)
%            Number of literals    :  326 (  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    :   65 (  65 usr;  21 con; 0-3 aty)
%            Number of variables   :  303 (  40 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments : Not in [Qua92]. Theorem SE3.1 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_sections_property3_1,negated_conjecture,
    well_ordering(xr,y) ).

cnf(prove_sections_property3_2,negated_conjecture,
    section(xr,w,y) ).

cnf(prove_sections_property3_3,negated_conjecture,
    ~ member(least(xr,intersection(complement(w),y)),y) ).

cnf(prove_sections_property3_4,negated_conjecture,
    y != w ).

%--------------------------------------------------------------------------