## TPTP Problem File: SET084+1.p

View Solutions - Solve Problem

```%--------------------------------------------------------------------------
% File     : SET084+1 : TPTP v8.0.0. Bugfixed v5.4.0.
% Domain   : Set Theory
% Problem  : A singleton set is determined by its element
% 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   : 0.25 v7.5.0, 0.28 v7.4.0, 0.17 v7.3.0, 0.24 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.27 v6.3.0, 0.33 v6.2.0, 0.44 v6.1.0, 0.40 v6.0.0, 0.43 v5.5.0, 0.37 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   ~;   3   |;  27   &)
%                                         (  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

% Bugfixed : v5.4.0 - Bugfixes to SET005+0 axiom file.
%--------------------------------------------------------------------------
%----Include set theory axioms
include('Axioms/SET005+0.ax').
%--------------------------------------------------------------------------
%----SS5: A singleton set is determined by its element
fof(singleton_identified_by_element2,conjecture,
! [X,Y] :
( ( singleton(X) = singleton(Y)
& member(Y,universal_class) )
=> X = Y ) ).

%--------------------------------------------------------------------------
```