TPTP Problem File: SET140-6.p
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- Solve Problem
%--------------------------------------------------------------------------
% File : SET140-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Domain : Set Theory
% Problem : Triple reduction 2
% Version : [Qua92] axioms.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% Source : [Quaife]
% Names : SB6.2 [Quaife]
% Status : Unsatisfiable
% Rating : 0.95 v8.2.0, 1.00 v2.1.0
% Syntax : Number of clauses : 93 ( 31 unt; 8 nHn; 63 RR)
% Number of literals : 183 ( 41 equ; 85 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% Number of functors : 41 ( 41 usr; 10 con; 0-3 aty)
% Number of variables : 178 ( 25 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments : The 'set builder' problems, of which this is one, do not appear
% in [Qua92]. In Quaife's development, these problems appear
% between the SINGLETON and the ORDERED PAIRS problems of [Qu92].
% However, in order to correspond to the paper, these theorems
% have not been used in the augmented versions of the subsequent
% problems in [Qua92].
% : Not in [Qua92].
% Bugfixes : v2.1.0 - Bugfix in SET004-0.ax.
%--------------------------------------------------------------------------
%----Include von Neuman-Bernays-Godel set theory axioms
include('Axioms/SET004-0.ax').
%--------------------------------------------------------------------------
%----(SBDEF1): definition of set builder.
cnf(definition_of_set_builder,axiom,
union(singleton(X),Y) = set_builder(X,Y) ).
cnf(prove_triple_reduction2_1,negated_conjecture,
set_builder(x,set_builder(y,set_builder(x,null_class))) != unordered_pair(x,y) ).
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