TPTP Problem File: SET862-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SET862-2 : TPTP v8.2.0. 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 : 0.30 v8.2.0, 0.33 v8.1.0, 0.32 v7.4.0, 0.35 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.20 v6.3.0, 0.18 v6.2.0, 0.20 v6.1.0, 0.50 v6.0.0, 0.40 v5.5.0, 0.70 v5.3.0, 0.72 v5.2.0, 0.62 v5.1.0, 0.65 v5.0.0, 0.57 v4.1.0, 0.54 v4.0.1, 0.45 v4.0.0, 0.55 v3.7.0, 0.40 v3.5.0, 0.45 v3.4.0, 0.50 v3.3.0, 0.43 v3.2.0
% Syntax : Number of clauses : 15 ( 3 unt; 3 nHn; 13 RR)
% Number of literals : 39 ( 2 equ; 22 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 0 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% 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__antisym_0,axiom,
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| V_A = V_B ) ).
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_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Set_OsubsetI_1,axiom,
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ) ).
cnf(cls_Zorn_Ochain__extend_0,axiom,
( ~ c_in(V_z,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_c,tc_set(T_a))
| c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Ochain__extend_1,axiom,
( ~ c_in(V_z,V_S,tc_set(T_a))
| ~ c_in(V_c,c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(V_c,V_z,T_a),V_z,tc_set(T_a))
| c_in(c_union(c_insert(V_z,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
( ~ c_in(V_z,V_x,T_a)
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(V_z,V_y,T_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_c,tc_set(T_a)) ) ).
cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
( ~ c_in(V_z,V_x,T_a)
| ~ c_in(V_c,c_Zorn_Omaxchain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(c_union(c_insert(V_x,c_emptyset,tc_set(T_a)),V_c,tc_set(T_a)),c_Zorn_Ochain(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(V_c,V_y,T_a),V_y,tc_set(T_a))
| c_in(V_z,V_y,T_a) ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_2,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_lessequals(V_U,v_y,tc_set(t_a))
| ~ c_in(V_U,v_c,tc_set(t_a)) ) ).
cnf(cls_conjecture_4,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_5,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_6,negated_conjecture,
( V_U != v_x(V_U)
| ~ c_in(V_U,v_S,tc_set(t_a)) ) ).
%------------------------------------------------------------------------------