%------------------------------------------------------------------------------
% File     : SET859-2 : TPTP v9.0.0. Released v3.2.0.
% Domain   : Set Theory
% Problem  : Problem about Zorn's lemma
% Version  : [Pau06] axioms : Reduced > Especial.
% English  :

% Refs     : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source   : [Pau06]
% Names    :

% Status   : Unsatisfiable
% Rating   : 0.00 v5.4.0, 0.06 v5.3.0, 0.05 v5.2.0, 0.00 v3.2.0
% Syntax   : Number of clauses     :    4 (   3 unt;   0 nHn;   3 RR)
%            Number of literals    :    6 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    1 (   1 usr;   0 prp; 3-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :    7 (   1 sgn)
% SPC      : CNF_UNS_RFO_NEQ_HRN

% Comments : The problems in the [Pau06] collection each have very many axioms,
%            of which only a small selection are required for the refutation.
%            The mission is to find those few axioms, after which a refutation
%            can be quite easily found. This version has only the necessary
%            axioms.
%------------------------------------------------------------------------------
cnf(cls_Set_Osubset__trans_0,axiom,
    ( ~ c_lessequals(V_B,V_C,tc_set(T_a))
    | ~ c_lessequals(V_A,V_B,tc_set(T_a))
    | c_lessequals(V_A,V_C,tc_set(T_a)) ) ).

cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
    c_lessequals(V_x,c_Zorn_Osucc(V_S,V_x,T_a),tc_set(tc_set(T_a))) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(c_Zorn_Osucc(v_S,v_n,t_a),v_m,tc_set(tc_set(t_a))) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))) ).

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