TPTP Problem File: SET096+1.p
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%------------------------------------------------------------------------------
% File : SET096+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Domain : Set Theory
% Problem : There are at most two subsets of a singleton set
% Version : [Qua92] axioms : Reduced & Augmented > Complete.
% English :
% Refs : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% Source : [Qua92]
% Names :
% Status : Theorem
% Rating : 0.56 v8.1.0, 0.53 v7.4.0, 0.47 v7.3.0, 0.55 v7.2.0, 0.52 v7.0.0, 0.53 v6.4.0, 0.50 v6.3.0, 0.58 v6.2.0, 0.60 v6.1.0, 0.73 v6.0.0, 0.70 v5.5.0, 0.74 v5.4.0
% Syntax : Number of formulae : 44 ( 16 unt; 0 def)
% Number of atoms : 103 ( 21 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 5 ~; 4 |; 26 &)
% ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 0 prp; 1-2 aty)
% Number of functors : 26 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 88 ( 83 !; 5 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
% Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
%------------------------------------------------------------------------------
%----Include set theory axioms
include('Axioms/SET005+0.ax').
%------------------------------------------------------------------------------
%----SS12
fof(two_subsets_of_singleton,conjecture,
! [X,Y] :
( subclass(X,singleton(Y))
=> ( X = null_class
| singleton(Y) = X ) ) ).
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