TPTP Problem File: SET845-2.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SET845-2 : 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 v5.3.0, 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 : 7 ( 4 unt; 0 nHn; 6 RR)
% Number of literals : 11 ( 3 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 2-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 12 ( 1 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.
%------------------------------------------------------------------------------
cnf(cls_Set_OUnion__upper_0,axiom,
( ~ c_in(V_B,V_A,tc_set(T_a))
| c_lessequals(V_B,c_Union(V_A,T_a),tc_set(T_a)) ) ).
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_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_OsuccI_0,axiom,
( ~ c_in(V_x,c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a)))
| c_in(c_Zorn_Osucc(V_S,V_x,T_a),c_Zorn_OTFin(V_S,T_a),tc_set(tc_set(T_a))) ) ).
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,
v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ).
cnf(cls_conjecture_2,negated_conjecture,
v_m != c_Zorn_Osucc(v_S,v_m,t_a) ).
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