TPTP Problem File: SEU149+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SEU149+1 : TPTP v8.2.0. Released v3.3.0.
% Domain : Set theory
% Problem : MPTP bushy problem t8_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-t8_zfmisc_1 [Urb07]
% Status : Theorem
% Rating : 0.14 v7.5.0, 0.16 v7.4.0, 0.03 v7.3.0, 0.07 v7.1.0, 0.09 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.20 v6.1.0, 0.23 v6.0.0, 0.22 v5.5.0, 0.15 v5.4.0, 0.18 v5.3.0, 0.22 v5.2.0, 0.00 v5.0.0, 0.17 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 14 ( 8 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 8 ( 1 ~; 1 |; 0 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 14 ( 14 !; 0 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments : Translated by MPTP 0.2 from the original problem in the Mizar
% library, www.mizar.org
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ) ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k2_tarski,axiom,
$true ).
fof(t8_zfmisc_1,conjecture,
! [A,B,C] :
( singleton(A) = unordered_pair(B,C)
=> A = B ) ).
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