TPTP Problem File: SET859-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SET859-1 : TPTP v8.2.0. Released v3.2.0.
% Domain : Set Theory
% Problem : Problem about Zorn's lemma
% Version : [Pau06] axioms : Especial.
% English :
% Refs : [Pau06] Paulson (2006), Email to G. Sutcliffe
% Source : [Pau06]
% Names : Zorn__TFin_subset_linear_simpler [Pau06]
% Status : Unsatisfiable
% Rating : 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, 0.10 v6.1.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.35 v5.3.0, 0.33 v5.2.0, 0.31 v5.1.0, 0.35 v5.0.0, 0.29 v4.1.0, 0.23 v4.0.1, 0.27 v4.0.0, 0.09 v3.7.0, 0.10 v3.5.0, 0.09 v3.4.0, 0.17 v3.3.0, 0.36 v3.2.0
% Syntax : Number of clauses : 1369 ( 222 unt; 33 nHn;1282 RR)
% Number of literals : 2594 ( 195 equ;1232 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 82 ( 81 usr; 0 prp; 1-3 aty)
% Number of functors : 127 ( 127 usr; 21 con; 0-6 aty)
% Number of variables : 1935 ( 211 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.
%------------------------------------------------------------------------------
include('Axioms/MSC001-2.ax').
include('Axioms/MSC001-0.ax').
%------------------------------------------------------------------------------
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_Zorn_OTFin__linear__lemma1_0,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a) != V_m
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_n,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(c_Zorn_Osucc(V_S,c_Zorn_OTFin__linear__lemma1__1(V_S,V_m,T_a),T_a),V_m,tc_set(tc_set(T_a)))
| c_lessequals(V_n,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_m,T_a),V_n,tc_set(tc_set(T_a))) ) ).
cnf(cls_Zorn_OTFin__linear__lemma2_0,axiom,
( ~ c_in(V_U,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_in(V_m,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| ~ c_lessequals(V_U,V_m,tc_set(tc_set(T_a)))
| c_lessequals(c_Zorn_Osucc(V_S,V_U,T_a),V_m,tc_set(tc_set(T_a)))
| V_U = V_m ) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,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))) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))) ).
%------------------------------------------------------------------------------