TPTP Problem File: SEU164+3.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEU164+3 : TPTP v9.0.0. Bugfixed v4.0.0.
% Domain : Set theory
% Problem : Basic properties of sets, theorem 99
% Version : [Urb06] axioms : Especial.
% English :
% Refs : [Byl90] Bylinski (1990), Some Basic Properties of Sets
% : [Urb06] Urban (2006), Email to G. Sutcliffe
% Source : [Urb06]
% Names : zfmisc_1__t99_zfmisc_1 [Urb06]
% Status : Theorem
% Rating : 0.39 v9.0.0, 0.44 v8.1.0, 0.42 v7.5.0, 0.38 v7.4.0, 0.43 v7.3.0, 0.38 v7.2.0, 0.34 v7.1.0, 0.35 v7.0.0, 0.40 v6.4.0, 0.38 v6.3.0, 0.42 v6.2.0, 0.52 v6.1.0, 0.67 v6.0.0, 0.52 v5.5.0, 0.56 v5.4.0, 0.61 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.52 v5.0.0, 0.54 v4.1.0, 0.61 v4.0.0
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 24 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 15 ( 2 ~; 0 |; 1 &)
% ( 9 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-2 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-1 aty)
% Number of variables : 25 ( 22 !; 3 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% library, www.mizar.org
% Bugfixes : v4.0.0 - Removed duplicate formula t2_tarski
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(C,D)
& in(D,A) ) ) ) ).
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ) ).
fof(t99_zfmisc_1,conjecture,
! [A] : union(powerset(A)) = A ).
%------------------------------------------------------------------------------