TPTP Problem File: SEU791^2.p
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% File : SEU791^2 : TPTP v8.2.0. Released v3.7.0.
% Domain : Set Theory
% Problem : Binary Relations on a Set - Second Wizard of Oz Examples
% Version : Especial > Reduced > Especial.
% English : (! A:i.! R:i.breln1 A R -> (! S:i.breln1 A S ->
% (! T:i.breln1 A T -> breln1compset A (binunion R S) T =
% binunion (breln1compset A R T) (breln1compset A S T))))
% Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% Source : [Bro08]
% Names : ZFC293l [Bro08]
% Status : Theorem
% Rating : 1.00 v7.4.0, 0.78 v7.2.0, 0.75 v7.0.0, 1.00 v3.7.0
% Syntax : Number of formulae : 25 ( 9 unt; 15 typ; 9 def)
% Number of atoms : 82 ( 11 equ; 0 cnn)
% Maximal formula atoms : 13 ( 8 avg)
% Number of connectives : 220 ( 0 ~; 1 |; 2 &; 166 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 44 ( 0 ^; 43 !; 1 ?; 44 :)
% SPC : TH0_THM_EQU_NAR
% Comments : http://mathgate.info/detsetitem.php?id=356
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thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(subbreln1_type,type,
subbreln1: $o ).
thf(subbreln1,definition,
( subbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ) ).
thf(breln1compset_type,type,
breln1compset: $i > $i > $i > $i ).
thf(breln1compprop_type,type,
breln1compprop: $o ).
thf(breln1compprop,definition,
( breln1compprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ).
thf(breln1compI_type,type,
breln1compI: $o ).
thf(breln1compI,definition,
( breln1compI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ) ).
thf(breln1compE_type,type,
breln1compE: $o ).
thf(breln1compE,definition,
( breln1compE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
thf(breln1unionprop_type,type,
breln1unionprop: $o ).
thf(breln1unionprop,definition,
( breln1unionprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ) ).
thf(breln1unionIL_type,type,
breln1unionIL: $o ).
thf(breln1unionIL,definition,
( breln1unionIL
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
thf(breln1unionIR_type,type,
breln1unionIR: $o ).
thf(breln1unionIR,definition,
( breln1unionIR
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ) ).
thf(breln1unionE_type,type,
breln1unionE: $o ).
thf(breln1unionE,definition,
( breln1unionE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ) ).
thf(woz2A,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionE
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
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