TSTP Solution File: SEV212^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV212^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qls7Fw4nC7 true
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:00:02 EDT 2023
% Result : Theorem 50.95s 7.49s
% Output : Refutation 50.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 34
% Syntax : Number of formulae : 137 ( 4 unt; 19 typ; 0 def)
% Number of atoms : 1161 ( 594 equ; 0 cnn)
% Maximal formula atoms : 69 ( 9 avg)
% Number of connectives : 3950 ( 75 ~; 290 |; 472 &;2565 @)
% ( 0 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 15 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 379 ( 379 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 8 con; 0-3 aty)
% ( 143 !!; 309 ??; 0 @@+; 0 @@-)
% Number of variables : 715 ( 452 ^; 227 !; 36 ?; 715 :)
% Comments :
%------------------------------------------------------------------------------
thf(iS_type,type,
iS: $tType ).
thf('#sk8_type',type,
'#sk8': iS ).
thf('#sk1_type',type,
'#sk1': iS ).
thf('#sk14_type',type,
'#sk14': iS ).
thf('#form1036_type',type,
'#form1036': ( iS > iS > iS > $o ) > $o ).
thf('#sk545_type',type,
'#sk545': ( iS > iS > iS > $o ) > iS ).
thf('#sk106_type',type,
'#sk106': ( iS > iS > iS > $o ) > iS ).
thf(c0_type,type,
c0: iS ).
thf('#sk637_type',type,
'#sk637': ( iS > iS > iS > $o ) > iS ).
thf('#sk851_type',type,
'#sk851': ( iS > iS > iS > $o ) > iS ).
thf('#sk463_type',type,
'#sk463': ( iS > iS > iS > $o ) > iS ).
thf('#sk739_type',type,
'#sk739': ( iS > iS > iS > $o ) > iS ).
thf('#sk391_type',type,
'#sk391': ( iS > iS > iS > $o ) > iS ).
thf('#sk2_type',type,
'#sk2': iS ).
thf(cP_type,type,
cP: iS > iS > iS ).
thf('#sk72_type',type,
'#sk72': ( iS > iS > iS > $o ) > iS ).
thf('#form1091_type',type,
'#form1091': ( iS > iS > iS > $o ) > $o ).
thf('#sk158_type',type,
'#sk158': ( iS > iS > iS > $o ) > iS ).
thf('#sk27_type',type,
'#sk27': iS > iS > iS > $o ).
thf(cS_LEM2_pme,conjecture,
( ( ! [X: iS > $o] :
( ( ! [Xx: iS,Xy: iS] :
( ( ( X @ Xy )
& ( X @ Xx ) )
=> ( X @ ( cP @ Xx @ Xy ) ) )
& ( X @ c0 ) )
=> ! [Xx: iS] : ( X @ Xx ) )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xu = Xv )
& ( Xx = Xy ) ) )
& ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 ) )
=> ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ Xu @ Xv @ Xv ) )
& ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ Xx @ Xy @ Xy ) ) )
=> ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ! [X: iS > $o] :
( ( ! [Xx: iS,Xy: iS] :
( ( ( X @ Xy )
& ( X @ Xx ) )
=> ( X @ ( cP @ Xx @ Xy ) ) )
& ( X @ c0 ) )
=> ! [Xx: iS] : ( X @ Xx ) )
& ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ( cP @ Xx @ Xu )
= ( cP @ Xy @ Xv ) )
=> ( ( Xu = Xv )
& ( Xx = Xy ) ) )
& ! [Xx: iS,Xy: iS] :
( ( cP @ Xx @ Xy )
!= c0 ) )
=> ! [Xx: iS,Xy: iS,Xu: iS,Xv: iS] :
( ( ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ Xu @ Xv @ Xv ) )
& ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ Xx @ Xy @ Xy ) ) )
=> ! [R: iS > iS > iS > $o] :
( ! [Xa: iS,Xb: iS,Xc: iS] :
( ( ? [Xx1: iS,Xx2: iS,Xy1: iS,Xy2: iS,Xz1: iS,Xz2: iS] :
( ( Xa
= ( cP @ Xx1 @ Xx2 ) )
& ( Xb
= ( cP @ Xy1 @ Xy2 ) )
& ( Xc
= ( cP @ Xz1 @ Xz2 ) )
& ( R @ Xx1 @ Xy1 @ Xz1 )
& ( R @ Xx2 @ Xy2 @ Xz2 ) )
| ( ( Xa = Xc )
& ( Xb = c0 ) )
| ( ( Xb = Xc )
& ( Xa = c0 ) ) )
=> ( R @ Xa @ Xb @ Xc ) )
=> ( R @ ( cP @ Xx @ Xu ) @ ( cP @ Xy @ Xv ) @ ( cP @ Xy @ Xv ) ) ) ) ),
inference('cnf.neg',[status(esa)],[cS_LEM2_pme]) ).
thf(zip_derived_cl0,plain,
~ ( ( ( !!
@ ^ [Y0: iS > $o] :
( ( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( Y0 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ ( cP @ Y1 @ Y2 ) ) ) ) )
& ( Y0 @ c0 ) )
=> ( !!
@ ^ [Y1: iS] : ( Y0 @ Y1 ) ) ) )
& ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( cP @ Y0 @ Y2 )
= ( cP @ Y1 @ Y3 ) )
=> ( ( Y2 = Y3 )
& ( Y0 = Y1 ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( cP @ Y0 @ Y1 )
!= c0 ) ) ) )
=> ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 @ Y3 ) ) )
& ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y1 @ Y3 ) @ ( cP @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 @ Y3 ) ) )
& ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ Y0 @ Y1 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y4: iS > iS > iS > $o] :
( ( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( !!
@ ^ [Y7: iS] :
( ( ( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ??
@ ^ [Y13: iS] :
( ( Y5
= ( cP @ Y8 @ Y9 ) )
& ( Y6
= ( cP @ Y10 @ Y11 ) )
& ( Y7
= ( cP @ Y12 @ Y13 ) )
& ( Y4 @ Y8 @ Y10 @ Y12 )
& ( Y4 @ Y9 @ Y11 @ Y13 ) ) ) ) ) ) ) )
| ( ( Y5 = Y7 )
& ( Y6 = c0 ) )
| ( ( Y6 = Y7 )
& ( Y5 = c0 ) ) )
=> ( Y4 @ Y5 @ Y6 @ Y7 ) ) ) ) )
=> ( Y4 @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y1 @ Y3 ) @ ( cP @ Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( !!
@ ^ [Y3: iS > iS > iS > $o] :
( ( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( ( ( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ( Y4
= ( cP @ Y7 @ Y8 ) )
& ( Y5
= ( cP @ Y9 @ Y10 ) )
& ( Y6
= ( cP @ Y11 @ Y12 ) )
& ( Y3 @ Y7 @ Y9 @ Y11 )
& ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
| ( ( Y4 = Y6 )
& ( Y5 = c0 ) )
| ( ( Y5 = Y6 )
& ( Y4 = c0 ) ) )
=> ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 @ Y2 ) ) )
& ( !!
@ ^ [Y3: iS > iS > iS > $o] :
( ( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( ( ( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ( Y4
= ( cP @ Y7 @ Y8 ) )
& ( Y5
= ( cP @ Y9 @ Y10 ) )
& ( Y6
= ( cP @ Y11 @ Y12 ) )
& ( Y3 @ Y7 @ Y9 @ Y11 )
& ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
| ( ( Y4 = Y6 )
& ( Y5 = c0 ) )
| ( ( Y5 = Y6 )
& ( Y4 = c0 ) ) )
=> ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y3 @ '#sk1' @ Y0 @ Y0 ) ) ) )
=> ( !!
@ ^ [Y3: iS > iS > iS > $o] :
( ( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( !!
@ ^ [Y6: iS] :
( ( ( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ??
@ ^ [Y12: iS] :
( ( Y4
= ( cP @ Y7 @ Y8 ) )
& ( Y5
= ( cP @ Y9 @ Y10 ) )
& ( Y6
= ( cP @ Y11 @ Y12 ) )
& ( Y3 @ Y7 @ Y9 @ Y11 )
& ( Y3 @ Y8 @ Y10 @ Y12 ) ) ) ) ) ) ) )
| ( ( Y4 = Y6 )
& ( Y5 = c0 ) )
| ( ( Y5 = Y6 )
& ( Y4 = c0 ) ) )
=> ( Y3 @ Y4 @ Y5 @ Y6 ) ) ) ) )
=> ( Y3 @ ( cP @ '#sk1' @ Y1 ) @ ( cP @ Y0 @ Y2 ) @ ( cP @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( ( !!
@ ^ [Y2: iS > iS > iS > $o] :
( ( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( ( ( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ( Y3
= ( cP @ Y6 @ Y7 ) )
& ( Y4
= ( cP @ Y8 @ Y9 ) )
& ( Y5
= ( cP @ Y10 @ Y11 ) )
& ( Y2 @ Y6 @ Y8 @ Y10 )
& ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
| ( ( Y3 = Y5 )
& ( Y4 = c0 ) )
| ( ( Y4 = Y5 )
& ( Y3 = c0 ) ) )
=> ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 @ Y1 ) ) )
& ( !!
@ ^ [Y2: iS > iS > iS > $o] :
( ( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( ( ( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ( Y3
= ( cP @ Y6 @ Y7 ) )
& ( Y4
= ( cP @ Y8 @ Y9 ) )
& ( Y5
= ( cP @ Y10 @ Y11 ) )
& ( Y2 @ Y6 @ Y8 @ Y10 )
& ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
| ( ( Y3 = Y5 )
& ( Y4 = c0 ) )
| ( ( Y4 = Y5 )
& ( Y3 = c0 ) ) )
=> ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y2 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
=> ( !!
@ ^ [Y2: iS > iS > iS > $o] :
( ( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( !!
@ ^ [Y5: iS] :
( ( ( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ??
@ ^ [Y11: iS] :
( ( Y3
= ( cP @ Y6 @ Y7 ) )
& ( Y4
= ( cP @ Y8 @ Y9 ) )
& ( Y5
= ( cP @ Y10 @ Y11 ) )
& ( Y2 @ Y6 @ Y8 @ Y10 )
& ( Y2 @ Y7 @ Y9 @ Y11 ) ) ) ) ) ) ) )
| ( ( Y3 = Y5 )
& ( Y4 = c0 ) )
| ( ( Y4 = Y5 )
& ( Y3 = c0 ) ) )
=> ( Y2 @ Y3 @ Y4 @ Y5 ) ) ) ) )
=> ( Y2 @ ( cP @ '#sk1' @ Y0 ) @ ( cP @ '#sk2' @ Y1 ) @ ( cP @ '#sk2' @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
~ ( !!
@ ^ [Y0: iS] :
( ( ( !!
@ ^ [Y1: iS > iS > iS > $o] :
( ( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( ( ( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ( Y2
= ( cP @ Y5 @ Y6 ) )
& ( Y3
= ( cP @ Y7 @ Y8 ) )
& ( Y4
= ( cP @ Y9 @ Y10 ) )
& ( Y1 @ Y5 @ Y7 @ Y9 )
& ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
| ( ( Y2 = Y4 )
& ( Y3 = c0 ) )
| ( ( Y3 = Y4 )
& ( Y2 = c0 ) ) )
=> ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y1 @ '#sk8' @ Y0 @ Y0 ) ) )
& ( !!
@ ^ [Y1: iS > iS > iS > $o] :
( ( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( ( ( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ( Y2
= ( cP @ Y5 @ Y6 ) )
& ( Y3
= ( cP @ Y7 @ Y8 ) )
& ( Y4
= ( cP @ Y9 @ Y10 ) )
& ( Y1 @ Y5 @ Y7 @ Y9 )
& ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
| ( ( Y2 = Y4 )
& ( Y3 = c0 ) )
| ( ( Y3 = Y4 )
& ( Y2 = c0 ) ) )
=> ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y1 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
=> ( !!
@ ^ [Y1: iS > iS > iS > $o] :
( ( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( !!
@ ^ [Y4: iS] :
( ( ( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ??
@ ^ [Y10: iS] :
( ( Y2
= ( cP @ Y5 @ Y6 ) )
& ( Y3
= ( cP @ Y7 @ Y8 ) )
& ( Y4
= ( cP @ Y9 @ Y10 ) )
& ( Y1 @ Y5 @ Y7 @ Y9 )
& ( Y1 @ Y6 @ Y8 @ Y10 ) ) ) ) ) ) ) )
| ( ( Y2 = Y4 )
& ( Y3 = c0 ) )
| ( ( Y3 = Y4 )
& ( Y2 = c0 ) ) )
=> ( Y1 @ Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y1 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ Y0 ) @ ( cP @ '#sk2' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl18,plain,
~ ( ( ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) )
& ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) )
=> ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl22,plain,
~ ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl27,plain,
~ ( ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( '#sk27' @ Y3 @ Y5 @ Y7 )
& ( '#sk27' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( '#sk27' @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( '#sk27' @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl38,plain,
~ ( '#sk27' @ ( cP @ '#sk1' @ '#sk8' ) @ ( cP @ '#sk2' @ '#sk14' ) @ ( cP @ '#sk2' @ '#sk14' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl37,plain,
( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( '#sk27' @ Y3 @ Y5 @ Y7 )
& ( '#sk27' @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( '#sk27' @ Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl46,plain,
! [X2: iS] :
( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( ( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ( X2
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( '#sk27' @ Y2 @ Y4 @ Y6 )
& ( '#sk27' @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( X2 = Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( X2 = c0 ) ) )
=> ( '#sk27' @ X2 @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl51,plain,
! [X2: iS,X4: iS] :
( !!
@ ^ [Y0: iS] :
( ( ( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ( X2
= ( cP @ Y1 @ Y2 ) )
& ( X4
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( '#sk27' @ Y1 @ Y3 @ Y5 )
& ( '#sk27' @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( X2 = Y0 )
& ( X4 = c0 ) )
| ( ( X4 = Y0 )
& ( X2 = c0 ) ) )
=> ( '#sk27' @ X2 @ X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl56,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk27' @ Y0 @ Y2 @ Y4 )
& ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
=> ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl59,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk27' @ Y0 @ Y2 @ Y4 )
& ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( ( X4 = X6 )
& ( X2 = c0 ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl66,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( X4 = X6 )
& ( X2 = c0 ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl71,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl77,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X4 != X6 )
| ( X2 != c0 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl78,plain,
! [X6: iS] : ( '#sk27' @ c0 @ X6 @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl65,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ( X2 = X6 )
& ( X4 = c0 ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl70,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl75,plain,
! [X2: iS,X4: iS,X6: iS] :
( ( X2 != X6 )
| ( X4 != c0 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl76,plain,
! [X6: iS] : ( '#sk27' @ X6 @ c0 @ X6 ),
inference(simplify,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl21,plain,
( ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) )
& ( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk8' @ '#sk14' @ '#sk14' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl33,plain,
! [X2: iS > iS > iS > $o] :
( ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl44,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl49,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( ( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl54,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( ( ( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= Y0 )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= Y0 )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl57,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( ( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl60,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl67,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl72,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ Y0 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl79,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk463' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl82,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ Y0 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk463' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl85,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl88,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl91,plain,
! [X2: iS > iS > iS > $o] :
( ( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl94,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl105,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl106,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl107,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
| ~ ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl120,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
| ~ ( '#form1091' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl26,plain,
( !!
@ ^ [Y0: iS > iS > iS > $o] :
( ( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( !!
@ ^ [Y3: iS] :
( ( ( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ??
@ ^ [Y9: iS] :
( ( Y1
= ( cP @ Y4 @ Y5 ) )
& ( Y2
= ( cP @ Y6 @ Y7 ) )
& ( Y3
= ( cP @ Y8 @ Y9 ) )
& ( Y0 @ Y4 @ Y6 @ Y8 )
& ( Y0 @ Y5 @ Y7 @ Y9 ) ) ) ) ) ) ) )
| ( ( Y1 = Y3 )
& ( Y2 = c0 ) )
| ( ( Y2 = Y3 )
& ( Y1 = c0 ) ) )
=> ( Y0 @ Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y0 @ '#sk1' @ '#sk2' @ '#sk2' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl35,plain,
! [X2: iS > iS > iS > $o] :
( ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl45,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( !!
@ ^ [Y2: iS] :
( ( ( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ??
@ ^ [Y8: iS] :
( ( Y0
= ( cP @ Y3 @ Y4 ) )
& ( Y1
= ( cP @ Y5 @ Y6 ) )
& ( Y2
= ( cP @ Y7 @ Y8 ) )
& ( X2 @ Y3 @ Y5 @ Y7 )
& ( X2 @ Y4 @ Y6 @ Y8 ) ) ) ) ) ) ) )
| ( ( Y0 = Y2 )
& ( Y1 = c0 ) )
| ( ( Y1 = Y2 )
& ( Y0 = c0 ) ) )
=> ( X2 @ Y0 @ Y1 @ Y2 ) ) ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl50,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( !!
@ ^ [Y1: iS] :
( ( ( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ??
@ ^ [Y7: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( Y0
= ( cP @ Y4 @ Y5 ) )
& ( Y1
= ( cP @ Y6 @ Y7 ) )
& ( X2 @ Y2 @ Y4 @ Y6 )
& ( X2 @ Y3 @ Y5 @ Y7 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= Y1 )
& ( Y0 = c0 ) )
| ( ( Y0 = Y1 )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ Y0 @ Y1 ) ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl55,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( !!
@ ^ [Y0: iS] :
( ( ( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ??
@ ^ [Y6: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( Y0
= ( cP @ Y5 @ Y6 ) )
& ( X2 @ Y1 @ Y3 @ Y5 )
& ( X2 @ Y2 @ Y4 @ Y6 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= Y0 )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= Y0 )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl58,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( ( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) )
=> ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl62,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl68,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y4 @ Y5 ) )
& ( X2 @ Y0 @ Y2 @ Y4 )
& ( X2 @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl73,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ Y0 ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y3 @ Y4 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ Y1 @ Y3 )
& ( X2 @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl80,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y2 @ Y3 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ Y0 @ Y2 )
& ( X2 @ ( '#sk463' @ X2 ) @ Y1 @ Y3 ) ) ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl83,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ Y0 ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y1 @ Y2 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y1 )
& ( X2 @ ( '#sk463' @ X2 ) @ Y0 @ Y2 ) ) ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl86,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ Y0 @ Y1 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ Y0 )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y1 ) ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl89,plain,
! [X2: iS > iS > iS > $o] :
( ( ??
@ ^ [Y0: iS] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ Y0 ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ Y0 ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl92,plain,
! [X2: iS > iS > iS > $o] :
( ( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl99,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl100,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
| ~ ( '#form1036' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl117,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
| ~ ( '#form1036' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl92_001,plain,
! [X2: iS > iS > iS > $o] :
( ( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl99_002,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl102,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl92,zip_derived_cl99]) ).
thf(zip_derived_cl106_003,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl116,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
& ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
& ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
& ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
& ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1036' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl102,zip_derived_cl106]) ).
thf(zip_derived_cl126,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl131,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl101,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= c0 )
| ~ ( '#form1036' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl118,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= c0 )
| ~ ( '#form1036' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl63,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl127,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl132,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl105_004,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl106_005,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl109,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl105,zip_derived_cl106]) ).
thf(zip_derived_cl99_006,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl119,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( ( '#sk72' @ X2 )
= ( cP @ ( '#sk391' @ X2 ) @ ( '#sk463' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( '#form1091' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl109,zip_derived_cl99]) ).
thf(zip_derived_cl108,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= c0 )
| ~ ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl121,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk72' @ X2 )
= c0 )
| ~ ( '#form1091' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl128,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl133,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl61,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( X2 @ ( '#sk72' @ X2 ) @ ( '#sk106' @ X2 ) @ ( '#sk158' @ X2 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl95,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl110,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl106_007,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl111,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl110,zip_derived_cl106]) ).
thf(zip_derived_cl99_008,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl122,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( ( '#sk106' @ X2 )
= ( cP @ ( '#sk545' @ X2 ) @ ( '#sk637' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( '#form1091' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl111,zip_derived_cl99]) ).
thf(zip_derived_cl129,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl96,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl112,plain,
! [X2: iS > iS > iS > $o] :
( ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl106_009,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl113,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl112,zip_derived_cl106]) ).
thf(zip_derived_cl99_010,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( ( '#sk158' @ X2 )
= ( cP @ ( '#sk739' @ X2 ) @ ( '#sk851' @ X2 ) ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( '#form1091' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl113,zip_derived_cl99]) ).
thf(zip_derived_cl130,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
| ( '#form1036' @ X2 )
| ( X2 @ '#sk1' @ '#sk2' @ '#sk2' )
| ( '#form1091' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl97,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl106_011,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl114,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl97,zip_derived_cl106]) ).
thf(zip_derived_cl99_012,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl124,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( X2 @ ( '#sk391' @ X2 ) @ ( '#sk545' @ X2 ) @ ( '#sk739' @ X2 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( '#form1091' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl114,zip_derived_cl99]) ).
thf(zip_derived_cl98,plain,
! [X2: iS > iS > iS > $o] :
( ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl106_013,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1091' @ X2 )
| ( ( ( '#sk106' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk72' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl115,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1091' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl98,zip_derived_cl106]) ).
thf(zip_derived_cl99_014,plain,
! [X2: iS > iS > iS > $o] :
( ~ ( '#form1036' @ X2 )
| ( ( ( '#sk72' @ X2 )
= ( '#sk158' @ X2 ) )
& ( ( '#sk106' @ X2 )
= c0 ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl125,plain,
! [X2: iS > iS > iS > $o] :
( ( '#form1036' @ X2 )
| ( X2 @ ( '#sk463' @ X2 ) @ ( '#sk637' @ X2 ) @ ( '#sk851' @ X2 ) )
| ( X2 @ '#sk8' @ '#sk14' @ '#sk14' )
| ( '#form1091' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl115,zip_derived_cl99]) ).
thf(zip_derived_cl64,plain,
! [X2: iS,X4: iS,X6: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ??
@ ^ [Y5: iS] :
( ( X2
= ( cP @ Y0 @ Y1 ) )
& ( X4
= ( cP @ Y2 @ Y3 ) )
& ( X6
= ( cP @ Y4 @ Y5 ) )
& ( '#sk27' @ Y0 @ Y2 @ Y4 )
& ( '#sk27' @ Y1 @ Y3 @ Y5 ) ) ) ) ) ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl69,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ??
@ ^ [Y4: iS] :
( ( X2
= ( cP @ X8 @ Y0 ) )
& ( X4
= ( cP @ Y1 @ Y2 ) )
& ( X6
= ( cP @ Y3 @ Y4 ) )
& ( '#sk27' @ X8 @ Y1 @ Y3 )
& ( '#sk27' @ Y0 @ Y2 @ Y4 ) ) ) ) ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl74,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ??
@ ^ [Y3: iS] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ Y0 @ Y1 ) )
& ( X6
= ( cP @ Y2 @ Y3 ) )
& ( '#sk27' @ X8 @ Y0 @ Y2 )
& ( '#sk27' @ X10 @ Y1 @ Y3 ) ) ) ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl81,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ??
@ ^ [Y2: iS] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ Y0 ) )
& ( X6
= ( cP @ Y1 @ Y2 ) )
& ( '#sk27' @ X8 @ X12 @ Y1 )
& ( '#sk27' @ X10 @ Y0 @ Y2 ) ) ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl84,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ??
@ ^ [Y1: iS] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ Y0 @ Y1 ) )
& ( '#sk27' @ X8 @ X12 @ Y0 )
& ( '#sk27' @ X10 @ X14 @ Y1 ) ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl87,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS] :
( ~ ( ??
@ ^ [Y0: iS] :
( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ X16 @ Y0 ) )
& ( '#sk27' @ X8 @ X12 @ X16 )
& ( '#sk27' @ X10 @ X14 @ Y0 ) ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl90,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ~ ( ( X2
= ( cP @ X8 @ X10 ) )
& ( X4
= ( cP @ X12 @ X14 ) )
& ( X6
= ( cP @ X16 @ X18 ) )
& ( '#sk27' @ X8 @ X12 @ X16 )
& ( '#sk27' @ X10 @ X14 @ X18 ) )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl93,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk27' @ X8 @ X12 @ X16 )
| ~ ( '#sk27' @ X10 @ X14 @ X18 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl103,plain,
! [X2: iS,X4: iS,X6: iS,X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ( X2
!= ( cP @ X8 @ X10 ) )
| ( X4
!= ( cP @ X12 @ X14 ) )
| ( X6
!= ( cP @ X16 @ X18 ) )
| ~ ( '#sk27' @ X8 @ X12 @ X16 )
| ~ ( '#sk27' @ X10 @ X14 @ X18 )
| ( '#sk27' @ X2 @ X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl104,plain,
! [X8: iS,X10: iS,X12: iS,X14: iS,X16: iS,X18: iS] :
( ( '#sk27' @ ( cP @ X8 @ X10 ) @ ( cP @ X12 @ X14 ) @ ( cP @ X16 @ X18 ) )
| ~ ( '#sk27' @ X10 @ X14 @ X18 )
| ~ ( '#sk27' @ X8 @ X12 @ X16 ) ),
inference(simplify,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl7264,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl38,zip_derived_cl78,zip_derived_cl76,zip_derived_cl120,zip_derived_cl117,zip_derived_cl131,zip_derived_cl118,zip_derived_cl63,zip_derived_cl132,zip_derived_cl119,zip_derived_cl121,zip_derived_cl133,zip_derived_cl61,zip_derived_cl122,zip_derived_cl129,zip_derived_cl123,zip_derived_cl130,zip_derived_cl124,zip_derived_cl125,zip_derived_cl104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEV212^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Qls7Fw4nC7 true
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 24 03:05:53 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.22/0.69 % Total configuration time : 828
% 0.22/0.69 % Estimated wc time : 1656
% 0.22/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 50.95/7.49 % Solved by lams/20_acsne_simpl.sh.
% 50.95/7.49 % done 617 iterations in 6.598s
% 50.95/7.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 50.95/7.49 % SZS output start Refutation
% See solution above
% 50.95/7.50
% 50.95/7.50
% 50.95/7.50 % Terminating...
% 50.95/7.61 % Runner terminated.
% 50.95/7.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------