%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU684^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.r4szYX4xQW true
% Computer : n026.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 Oct 2 04:55:46 PM UTC 2025
% Result : Theorem 0.58s 0.85s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 71 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 430 ( 63 equ; 0 cnn)
% Maximal formula atoms : 39 ( 6 avg)
% Number of connectives : 1481 ( 42 ~; 24 |; 54 &;1176 @)
% ( 0 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 21 usr; 11 con; 0-4 aty)
% ( 67 !!; 23 ??; 0 @@+; 0 @@-)
% Number of variables : 304 ( 210 ^; 83 !; 11 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_type,type,
singleton: $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(funcImageSingleton_type,type,
funcImageSingleton: $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(theprop_type,type,
theprop: $o ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(ap,axiom,
( ap
= ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ).
thf('0',plain,
( ap
= ( ^ [A: $i,B: $i,Xf: $i,Xx: $i] :
( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ap]) ).
thf('1',plain,
( ap
= ( ^ [V_1: $i,V_2: $i,V_3: $i,V_4: $i] :
( setunion
@ ( dsetconstr @ V_2
@ ^ [V_5: $i] : ( in @ ( kpair @ V_4 @ V_5 ) @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf(funcImageSingleton,axiom,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
thf('2',plain,
( funcImageSingleton
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( singleton
@ ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(func,axiom,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
thf(breln,axiom,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf('3',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('4',plain,
( breln
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(ex1,axiom,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
thf(singleton,axiom,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ) ).
thf('5',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('6',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('7',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'6']) ).
thf('8',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('9',plain,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[func,'4','8','6']) ).
thf('10',plain,
( func
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( ( breln @ V_1 @ V_2 @ V_3 )
& ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( ex1 @ V_2
@ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
define([status(thm)]) ).
thf(theprop,axiom,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ) ).
thf('11',plain,
( theprop
= ( ! [X4: $i] :
( ( singleton @ X4 )
=> ( in @ ( setunion @ X4 ) @ X4 ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrER,axiom,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf('12',plain,
( dsetconstrER
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(funcGraphProp1,conjecture,
( dsetconstrER
=> ( theprop
=> ( funcImageSingleton
=> ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ( ! [X10: $i] :
( ? [X12: $i] :
( ( in @ X12 @ X10 )
& ( X10
= ( setadjoin @ X12 @ emptyset ) ) )
=> ( in @ ( setunion @ X10 ) @ X10 ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_2: $i] : ( in @ ( kpair @ X20 @ V_2 ) @ X18 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) )
& ( subset @ X18 @ ( cartprod @ X14 @ X16 ) ) )
=> ! [X24: $i] :
( ( in @ X24 @ X14 )
=> ? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ X16
@ ^ [V_5: $i] : ( in @ ( kpair @ X24 @ V_5 ) @ X18 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_4: $i] : ( in @ ( kpair @ X24 @ V_4 ) @ X18 ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) )
=> ! [X28: $i,X30: $i,X32: $i] :
( ( ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ? [X36: $i] :
( ( in @ X36
@ ( dsetconstr @ X30
@ ^ [V_7: $i] : ( in @ ( kpair @ X34 @ V_7 ) @ X32 ) ) )
& ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( in @ ( kpair @ X34 @ V_6 ) @ X32 ) )
= ( setadjoin @ X36 @ emptyset ) ) ) )
& ( subset @ X32 @ ( cartprod @ X28 @ X30 ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( in
@ ( kpair @ X38
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_8: $i] : ( in @ ( kpair @ X38 @ V_8 ) @ X32 ) ) ) )
@ X32 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ( ! [X10: $i] :
( ? [X12: $i] :
( ( in @ X12 @ X10 )
& ( X10
= ( setadjoin @ X12 @ emptyset ) ) )
=> ( in @ ( setunion @ X10 ) @ X10 ) )
=> ( ! [X14: $i,X16: $i,X18: $i] :
( ( ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ X16
@ ^ [V_3: $i] : ( in @ ( kpair @ X20 @ V_3 ) @ X18 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_2: $i] : ( in @ ( kpair @ X20 @ V_2 ) @ X18 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) )
& ( subset @ X18 @ ( cartprod @ X14 @ X16 ) ) )
=> ! [X24: $i] :
( ( in @ X24 @ X14 )
=> ? [X26: $i] :
( ( in @ X26
@ ( dsetconstr @ X16
@ ^ [V_5: $i] : ( in @ ( kpair @ X24 @ V_5 ) @ X18 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_4: $i] : ( in @ ( kpair @ X24 @ V_4 ) @ X18 ) )
= ( setadjoin @ X26 @ emptyset ) ) ) ) )
=> ! [X28: $i,X30: $i,X32: $i] :
( ( ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ? [X36: $i] :
( ( in @ X36
@ ( dsetconstr @ X30
@ ^ [V_7: $i] : ( in @ ( kpair @ X34 @ V_7 ) @ X32 ) ) )
& ( ( dsetconstr @ X30
@ ^ [V_6: $i] : ( in @ ( kpair @ X34 @ V_6 ) @ X32 ) )
= ( setadjoin @ X36 @ emptyset ) ) ) )
& ( subset @ X32 @ ( cartprod @ X28 @ X30 ) ) )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( in
@ ( kpair @ X38
@ ( setunion
@ ( dsetconstr @ X30
@ ^ [V_8: $i] : ( in @ ( kpair @ X38 @ V_8 ) @ X32 ) ) ) )
@ X32 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( Y0
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in
@ ( kpair @ Y3
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
@ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( Y0
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in
@ ( kpair @ Y3
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
@ Y2 ) ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( Y0
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in
@ ( kpair @ Y3
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
@ Y2 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( Y0
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in
@ ( kpair @ Y3
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
@ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in
@ ( kpair @ Y3
@ ( setunion
@ ( dsetconstr @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) )
@ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( in
@ ( kpair @ Y2
@ ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) )
@ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk4'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk4' ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( in
@ ( kpair @ Y1
@ ( setunion
@ ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) )
@ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk6' @ ( cartprod @ '#sk1' @ '#sk4' ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( in
@ ( kpair @ Y0
@ ( setunion
@ ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk6' ) ) ) )
@ '#sk6' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl18,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk6' @ ( cartprod @ '#sk1' @ '#sk4' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk6' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk6' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk6' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] :
( ( ( in @ ( '#sk9' @ X2 )
@ ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) ) )
& ( ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) )
= ( setadjoin @ ( '#sk9' @ X2 ) @ emptyset ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) )
= ( setadjoin @ ( '#sk9' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) )
= ( setadjoin @ ( '#sk9' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ( in @ ( '#sk9' @ X2 )
@ ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl79,plain,
! [X0: $i] :
( ( in @ ( '#sk9' @ X0 ) @ ( setadjoin @ ( '#sk9' @ X0 ) @ emptyset ) )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl32,zip_derived_cl30]) ).
thf(zip_derived_cl81,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ ( '#sk9' @ X0 ) @ ( setadjoin @ ( '#sk9' @ X0 ) @ emptyset ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( Y0
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( in @ ( setunion @ Y0 ) @ Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
! [X2: $i] :
( ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( X2
= ( setadjoin @ Y0 @ emptyset ) ) ) )
=> ( in @ ( setunion @ X2 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( X2
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ( in @ ( setunion @ X2 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ X4 @ X2 )
& ( X2
= ( setadjoin @ X4 @ emptyset ) ) )
| ( in @ ( setunion @ X2 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ X2 )
| ( X2
!= ( setadjoin @ X4 @ emptyset ) )
| ( in @ ( setunion @ X2 ) @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ X2 )
| ( X2
!= ( setadjoin @ X4 @ emptyset ) )
| ( in @ ( setunion @ X2 ) @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl21,plain,
! [X4: $i] :
( ( in @ ( setunion @ ( setadjoin @ X4 @ emptyset ) ) @ ( setadjoin @ X4 @ emptyset ) )
| ~ ( in @ X4 @ ( setadjoin @ X4 @ emptyset ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl32_001,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) )
= ( setadjoin @ ( '#sk9' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl5,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
=> ( X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
=> ( X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl75,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ ( setadjoin @ ( '#sk9' @ X0 ) @ emptyset ) )
| ~ ( in @ X0 @ '#sk1' )
| ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk6' )
@ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl14]) ).
thf(zip_derived_cl77,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ ( setadjoin @ ( '#sk9' @ X0 ) @ emptyset ) )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ ( kpair @ X0 @ X1 ) @ '#sk6' ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl32_002,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk6' ) )
= ( setadjoin @ ( '#sk9' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl19,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( in
@ ( kpair @ Y0
@ ( setunion
@ ( dsetconstr @ '#sk4'
@ ^ [Y1: $i] : ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk6' ) ) ) )
@ '#sk6' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl24,plain,
~ ( ( in @ '#sk8' @ '#sk1' )
=> ( in
@ ( kpair @ '#sk8'
@ ( setunion
@ ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk6' ) ) ) )
@ '#sk6' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl27,plain,
~ ( in
@ ( kpair @ '#sk8'
@ ( setunion
@ ( dsetconstr @ '#sk4'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk6' ) ) ) )
@ '#sk6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl74,plain,
( ~ ( in @ ( kpair @ '#sk8' @ ( setunion @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ) ) @ '#sk6' )
| ~ ( in @ '#sk8' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl27]) ).
thf(zip_derived_cl26,plain,
in @ '#sk8' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl76,plain,
~ ( in @ ( kpair @ '#sk8' @ ( setunion @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ) ) @ '#sk6' ),
inference(demod,[status(thm)],[zip_derived_cl74,zip_derived_cl26]) ).
thf(zip_derived_cl86,plain,
( ~ ( in @ '#sk8' @ '#sk1' )
| ~ ( in @ ( setunion @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ) @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl76]) ).
thf(zip_derived_cl26_003,plain,
in @ '#sk8' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl88,plain,
~ ( in @ ( setunion @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ) @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ),
inference(demod,[status(thm)],[zip_derived_cl86,zip_derived_cl26]) ).
thf(zip_derived_cl90,plain,
~ ( in @ ( '#sk9' @ '#sk8' ) @ ( setadjoin @ ( '#sk9' @ '#sk8' ) @ emptyset ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl88]) ).
thf(zip_derived_cl92,plain,
~ ( in @ '#sk8' @ '#sk1' ),
inference('sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl90]) ).
thf(zip_derived_cl26_004,plain,
in @ '#sk8' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl94,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl92,zip_derived_cl26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU684^2 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.r4szYX4xQW true
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:00:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in HO mode
% 0.55/0.69 % Total configuration time : 828
% 0.55/0.69 % Estimated wc time : 1656
% 0.55/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.55/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.58/0.85 % Solved by lams/20_acsne_simpl.sh.
% 0.58/0.85 % done 18 iterations in 0.054s
% 0.58/0.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.58/0.85 % SZS output start Refutation
% See solution above
% 0.58/0.86
% 0.58/0.86
% 0.58/0.86 % Terminating...
% 0.66/0.97 % Runner terminated.
% 0.66/0.98 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------