TPTP Problem File: SEU156+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : SEU156+1 : TPTP v9.0.0. Released v3.3.0.
% Domain : Set theory
% Problem : MPTP bushy problem t33_zfmisc_1
% Version : [Urb07] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co
% : [Urb07] Urban (2006), Email to G. Sutcliffe
% Source : [Urb07]
% Names : bushy-t33_zfmisc_1 [Urb07]
% Status : Theorem
% Rating : 0.36 v9.0.0, 0.42 v8.2.0, 0.36 v7.5.0, 0.47 v7.4.0, 0.30 v7.3.0, 0.31 v7.2.0, 0.28 v7.1.0, 0.26 v7.0.0, 0.30 v6.4.0, 0.35 v6.3.0, 0.29 v6.2.0, 0.36 v6.1.0, 0.40 v6.0.0, 0.35 v5.5.0, 0.37 v5.4.0, 0.43 v5.3.0, 0.44 v5.2.0, 0.30 v5.1.0, 0.33 v5.0.0, 0.38 v4.1.0, 0.39 v4.0.0, 0.42 v3.7.0, 0.45 v3.5.0, 0.42 v3.4.0, 0.53 v3.3.0
% Syntax : Number of formulae : 15 ( 10 unt; 0 def)
% Number of atoms : 22 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 5 ~; 0 |; 3 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 0 con; 1-2 aty)
% Number of variables : 27 ( 25 !; 2 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% library, www.mizar.org
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k2_tarski,axiom,
$true ).
fof(dt_k4_tarski,axiom,
$true ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(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(t10_zfmisc_1,axiom,
! [A,B,C,D] :
~ ( unordered_pair(A,B) = unordered_pair(C,D)
& A != C
& A != D ) ).
fof(t33_zfmisc_1,conjecture,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( A = C
& B = D ) ) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A) ).
fof(t6_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ) ).
fof(t8_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ) ).
fof(t9_zfmisc_1,axiom,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> B = C ) ).
%------------------------------------------------------------------------------