TPTP Problem File: SEU769^2.p
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% File : SEU769^2 : TPTP v9.0.0. Released v3.7.0.
% Domain : Set Theory
% Problem : Binary Relations on a Set
% Version : Especial > Reduced > Especial.
% English : (! A:i.! R:i.in R (breln1Set A) -> breln1 A R)
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC271l [Bro08]
% Status : Theorem
% Rating : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% Syntax : Number of formulae : 14 ( 4 unt; 9 typ; 4 def)
% Number of atoms : 14 ( 4 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 28 ( 0 ~; 0 |; 0 &; 25 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 9 usr; 1 con; 0-3 aty)
% Number of variables : 13 ( 8 ^; 5 !; 0 ?; 13 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=375
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thf(in_type,type,
in: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ) ).
thf(breln1Set_type,type,
breln1Set: $i > $i ).
thf(breln1Set,definition,
( breln1Set
= ( ^ [A: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ A @ A ) )
@ ^ [R: $i] : ( breln1 @ A @ R ) ) ) ) ).
thf(breln1SetBreln1,conjecture,
( dsetconstrER
=> ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) ) ).
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