TPTP Problem File: SET865-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SET865-2 : 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 : 0.08 v9.0.0, 0.06 v8.2.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.00 v5.3.0, 0.08 v5.2.0, 0.00 v5.1.0, 0.14 v4.1.0, 0.22 v4.0.1, 0.33 v3.7.0, 0.17 v3.3.0, 0.14 v3.2.0
% Syntax : Number of clauses : 8 ( 2 unt; 0 nHn; 6 RR)
% Number of literals : 17 ( 2 equ; 10 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_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.
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cnf(cls_conjecture_0,negated_conjecture,
( c_in(c_Union(V_U,t_a),v_S,tc_set(t_a))
| ~ c_in(V_U,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_x(V_U),v_S,tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(V_U,v_x(V_U),tc_set(t_a))
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_conjecture_3,negated_conjecture,
( V_U != v_x(V_U)
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
cnf(cls_Set_OsubsetD_0,axiom,
( ~ c_in(V_c,V_A,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(V_c,V_B,T_a) ) ).
cnf(cls_Zorn_OHausdorff_0,axiom,
c_in(c_Zorn_OHausdorff__1(V_S,T_a),c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a))) ).
cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
( ~ c_in(V_u,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Union(V_c,T_a),V_u,tc_set(T_a))
| c_Union(V_c,T_a) = V_u ) ).
cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
c_lessequals(c_Zorn_Omaxchain(V_S,T_a),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(tc_set(T_a)))) ).
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