TPTP Problem File: SET833-2.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : SET833-2 : TPTP v8.1.0. Released v3.2.0.
% Domain   : Set Theory
% Problem  : Problem about set theory
% 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, 0.10 v5.2.0, 0.00 v3.2.0
% Syntax   : Number of clauses     :    4 (   3 unt;   0 nHn;   4 RR)
%            Number of literals    :    6 (   0 equ;   3 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    2 (   2 usr;   0 prp; 3-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :    4 (   0 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_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_conjecture_1,negated_conjecture,
    c_lessequals(v_Z,v_V,tc_set(t_a)) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_in(v_x,v_Z,t_a) ).

cnf(cls_conjecture_3,negated_conjecture,
    ~ c_in(v_x,v_V,t_a) ).

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