TSTP Solution File: SEU655^2 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU655^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.h54dvJGBKg true
% Computer : n027.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 19:15:35 EDT 2023
% Result : Theorem 6.08s 1.52s
% Output : Refutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 34
% Syntax : Number of formulae : 138 ( 48 unt; 18 typ; 0 def)
% Number of atoms : 587 ( 320 equ; 0 cnn)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 3546 ( 103 ~; 99 |; 62 &;3068 @)
% ( 0 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 10 con; 0-2 aty)
% ( 64 !!; 40 ??; 0 @@+; 0 @@-)
% Number of variables : 360 ( 213 ^; 130 !; 17 ?; 360 :)
% Comments :
%------------------------------------------------------------------------------
thf(setukpairinjR_type,type,
setukpairinjR: $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(ex1I_type,type,
ex1I: $o ).
thf('#sk20_type',type,
'#sk20': $i ).
thf('#sk12_type',type,
'#sk12': $i ).
thf(iskpair_type,type,
iskpair: $i > $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(kfstpairEq_type,type,
kfstpairEq: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk103_type',type,
'#sk103': $i > $i > $i ).
thf(kfst_type,type,
kfst: $i > $i ).
thf('#sk104_type',type,
'#sk104': $i > $i ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(setukpairinjR,axiom,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ) ).
thf('0',plain,
( setukpairinjR
= ( ! [X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( kpair @ X4 @ X6 )
= ( kpair @ X8 @ X10 ) )
=> ( X6 = X10 ) ) ) ),
define([status(thm)]) ).
thf(kfstpairEq,axiom,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ).
thf('1',plain,
( kfstpairEq
= ( ! [X4: $i,X6: $i] :
( ( kfst @ ( kpair @ X4 @ X6 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(ex1I,axiom,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
thf('2',plain,
( ex1I
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( X6 @ X10 )
=> ( X10 = X8 ) ) )
=> ( ex1 @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) ) ) ) ) ),
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('3',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('4',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('5',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'4']) ).
thf('6',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf(kpair,axiom,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
thf('7',plain,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[kpair]) ).
thf('8',plain,
( kpair
= ( ^ [V_1: $i,V_2: $i] : ( setadjoin @ ( setadjoin @ V_1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ V_1 @ ( setadjoin @ V_2 @ emptyset ) ) @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ? [Xy: $i] :
( ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
& ( in @ Xy @ ( setunion @ A ) ) )
& ( in @ Xx @ ( setunion @ A ) ) ) ) ) ).
thf('9',plain,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ? [Xy: $i] :
( ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
& ( in @ Xy @ ( setunion @ A ) ) )
& ( in @ Xx @ ( setunion @ A ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iskpair]) ).
thf('10',plain,
( iskpair
= ( ^ [V_1: $i] :
? [X4: $i] :
( ? [X6: $i] :
( ( V_1
= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X6 @ ( setunion @ V_1 ) ) )
& ( in @ X4 @ ( setunion @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(ksndsingleton,conjecture,
( ex1I
=> ( kfstpairEq
=> ( setukpairinjR
=> ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( X6 @ X10 )
=> ( X10 = X8 ) ) )
=> ? [X12: $i] :
( ( in @ X12
@ ( dsetconstr @ X4
@ ^ [V_2: $i] : ( X6 @ V_2 ) ) )
& ( ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) )
= ( setadjoin @ X12 @ emptyset ) ) ) ) ) )
=> ( ! [X14: $i,X16: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) )
= X14 )
=> ( ! [X18: $i,X20: $i,X22: $i,X24: $i] :
( ( ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ emptyset ) ) )
=> ( X20 = X24 ) )
=> ! [X26: $i] :
( ? [X28: $i] :
( ( in @ X28 @ ( setunion @ X26 ) )
& ? [X30: $i] :
( ( in @ X30 @ ( setunion @ X26 ) )
& ( X26
= ( setadjoin @ ( setadjoin @ X28 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X28 @ ( setadjoin @ X30 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X32: $i] :
( ( in @ X32
@ ( dsetconstr @ ( setunion @ X26 )
@ ^ [V_4: $i] :
( X26
= ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ ( setadjoin @ V_4 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ X26 )
@ ^ [V_3: $i] :
( X26
= ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ ( setadjoin @ V_3 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ X32 @ emptyset ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( X6 @ X10 )
=> ( X10 = X8 ) ) )
=> ? [X12: $i] :
( ( in @ X12
@ ( dsetconstr @ X4
@ ^ [V_2: $i] : ( X6 @ V_2 ) ) )
& ( ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) )
= ( setadjoin @ X12 @ emptyset ) ) ) ) ) )
=> ( ! [X14: $i,X16: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X14 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X14 @ ( setadjoin @ X16 @ emptyset ) ) @ emptyset ) ) )
= X14 )
=> ( ! [X18: $i,X20: $i,X22: $i,X24: $i] :
( ( ( setadjoin @ ( setadjoin @ X18 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X18 @ ( setadjoin @ X20 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X22 @ ( setadjoin @ X24 @ emptyset ) ) @ emptyset ) ) )
=> ( X20 = X24 ) )
=> ! [X26: $i] :
( ? [X28: $i] :
( ( in @ X28 @ ( setunion @ X26 ) )
& ? [X30: $i] :
( ( in @ X30 @ ( setunion @ X26 ) )
& ( X26
= ( setadjoin @ ( setadjoin @ X28 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X28 @ ( setadjoin @ X30 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [X32: $i] :
( ( in @ X32
@ ( dsetconstr @ ( setunion @ X26 )
@ ^ [V_4: $i] :
( X26
= ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ ( setadjoin @ V_4 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ X26 )
@ ^ [V_3: $i] :
( X26
= ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ X26 ) @ ( setadjoin @ V_3 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ X32 @ emptyset ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y3 = Y2 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( Y1 @ Y4 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( Y1 @ Y4 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y3 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( Y0
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y3 = Y2 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( dsetconstr @ Y0 @ Y1 )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y3 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( Y0
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y3 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( Y0
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y3 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( Y0
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ Y0 ) )
& ( Y0
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ Y0 )
@ ^ [Y2: $i] :
( Y0
= ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ Y0 ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
~ ( ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ '#sk5' ) )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ '#sk5' ) )
& ( '#sk5'
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl18,plain,
( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ '#sk5' ) )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ '#sk5' ) )
& ( '#sk5'
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl22,plain,
( ( in @ '#sk12' @ ( setunion @ '#sk5' ) )
& ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ '#sk5' ) )
& ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl27,plain,
( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ '#sk5' ) )
& ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl31,plain,
( ( in @ '#sk20' @ ( setunion @ '#sk5' ) )
& ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl37,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl41,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y3 )
=> ( Y3 = Y2 ) ) ) )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( dsetconstr @ Y0 @ Y1 )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( Y0 @ Y2 )
=> ( Y2 = Y1 ) ) ) )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ X2 @ Y0 ) )
& ( ( dsetconstr @ X2 @ Y0 )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y1 )
=> ( Y1 = Y0 ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl54,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X0
@ ^ [Y2: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y2: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl56,plain,
! [X0: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
| ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X2: $i] :
( ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X2: $i] :
( ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl59,plain,
! [X0: $i,X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X2 ) ) ) )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( in @ X2 @ X0 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl60,plain,
! [X0: $i,X2: $i] :
( ~ ( ( in @ ( '#sk103' @ X0 @ X2 ) @ X0 )
=> ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
=> ( ( '#sk103' @ X0 @ X2 )
= X2 ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl62,plain,
! [X0: $i,X2: $i] :
( ~ ( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
=> ( ( '#sk103' @ X0 @ X2 )
= X2 ) )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( in @ X2 @ X0 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl65,plain,
! [X0: $i,X2: $i] :
( ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl70,plain,
! [X0: $i,X2: $i] :
( ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl71,plain,
! [X0: $i,X2: $i] :
( ( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl78,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl41_001,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
= Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl79,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_002,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl839,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl78,zip_derived_cl79,zip_derived_cl79]) ).
thf(zip_derived_cl846,plain,
! [X0: $i] :
( ( '#sk5' != '#sk5' )
| ~ ( in @ '#sk20' @ X0 )
| ( ( '#sk103' @ X0 @ '#sk20' )
!= '#sk20' )
| ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl839]) ).
thf(zip_derived_cl850,plain,
! [X0: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( ( '#sk103' @ X0 @ '#sk20' )
!= '#sk20' )
| ~ ( in @ '#sk20' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl846]) ).
thf(zip_derived_cl41_003,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl75,plain,
! [X0: $i,X2: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl79_004,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_005,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl705,plain,
! [X0: $i,X2: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( '#sk103' @ X0 @ X2 )
!= X2 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl79,zip_derived_cl79]) ).
thf(zip_derived_cl712,plain,
! [X0: $i] :
( ( '#sk5' != '#sk5' )
| ~ ( in @ '#sk20' @ X0 )
| ( ( '#sk103' @ X0 @ '#sk20' )
!= '#sk20' )
| ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl705]) ).
thf(zip_derived_cl716,plain,
! [X0: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( '#sk103' @ X0 @ '#sk20' )
!= '#sk20' )
| ~ ( in @ '#sk20' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl712]) ).
thf(zip_derived_cl19,plain,
~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
~ ( ( in @ X2
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl734,plain,
( ~ ( in @ '#sk20' @ ( setunion @ '#sk5' ) )
| ( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
!= '#sk20' )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl716,zip_derived_cl32]) ).
thf(zip_derived_cl36,plain,
in @ '#sk20' @ ( setunion @ '#sk5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl744,plain,
( ( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
!= '#sk20' )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl734,zip_derived_cl36]) ).
thf(zip_derived_cl36_006,plain,
in @ '#sk20' @ ( setunion @ '#sk5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl41_007,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl64,plain,
! [X0: $i,X2: $i] :
( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl68,plain,
! [X0: $i,X2: $i] :
( ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y1: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl69,plain,
! [X0: $i,X2: $i] :
( ( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl74,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl77,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl79_008,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_009,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_010,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_011,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl854,plain,
! [X0: $i,X2: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl77,zip_derived_cl79,zip_derived_cl79,zip_derived_cl79,zip_derived_cl79]) ).
thf(zip_derived_cl861,plain,
! [X0: $i] :
( ( '#sk5' != '#sk5' )
| ~ ( in @ '#sk20' @ X0 )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl854]) ).
thf(zip_derived_cl865,plain,
! [X0: $i] :
( ( ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ X0 ) @ emptyset ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ '#sk20' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl861]) ).
thf(zip_derived_cl869,plain,
( ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl865]) ).
thf(zip_derived_cl36_012,plain,
in @ '#sk20' @ ( setunion @ '#sk5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl41_013,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl73,plain,
! [X0: $i,X2: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl79_014,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_015,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_016,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl79_017,plain,
( ( kfst @ '#sk5' )
= '#sk12' ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl16]) ).
thf(zip_derived_cl602,plain,
! [X0: $i,X2: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ X2 ) @ emptyset ) ) @ emptyset ) ) )
| ( '#sk5'
!= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl73,zip_derived_cl79,zip_derived_cl79,zip_derived_cl79,zip_derived_cl79]) ).
thf(zip_derived_cl609,plain,
! [X0: $i] :
( ( '#sk5' != '#sk5' )
| ~ ( in @ '#sk20' @ X0 )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl602]) ).
thf(zip_derived_cl613,plain,
! [X0: $i] :
( ( in @ ( '#sk104' @ X0 )
@ ( dsetconstr @ X0
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ X0 @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ '#sk20' @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl609]) ).
thf(zip_derived_cl619,plain,
( ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ( in @ ( '#sk104' @ ( setunion @ '#sk5' ) )
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl613]) ).
thf(zip_derived_cl32_018,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl720,plain,
( ( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl619,zip_derived_cl32]) ).
thf(zip_derived_cl871,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' ) @ emptyset ) ) @ emptyset ) ) ),
inference(clc,[status(thm)],[zip_derived_cl869,zip_derived_cl720]) ).
thf(zip_derived_cl41_019,plain,
( '#sk5'
= ( setadjoin @ ( setadjoin @ '#sk12' @ emptyset ) @ ( setadjoin @ ( setadjoin @ '#sk12' @ ( setadjoin @ '#sk20' @ emptyset ) ) @ emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( !!
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y3 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = Y2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i,X6: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X6 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X6 @ ( setadjoin @ X8 @ emptyset ) ) @ emptyset ) ) )
=> ( X4 = X8 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X6 @ ( setadjoin @ X8 @ emptyset ) ) @ emptyset ) ) )
| ( X4 = X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X6 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X6 @ ( setadjoin @ X8 @ emptyset ) ) @ emptyset ) ) )
| ( X4 = X8 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl148,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) )
!= '#sk5' )
| ( X0 = '#sk20' ) ),
inference('sup-',[status(thm)],[zip_derived_cl41,zip_derived_cl35]) ).
thf(zip_derived_cl883,plain,
( ( '#sk5' != '#sk5' )
| ( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
= '#sk20' ) ),
inference('sup-',[status(thm)],[zip_derived_cl871,zip_derived_cl148]) ).
thf(zip_derived_cl946,plain,
( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
= '#sk20' ),
inference(simplify,[status(thm)],[zip_derived_cl883]) ).
thf(zip_derived_cl974,plain,
( ( '#sk20' != '#sk20' )
| ( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl744,zip_derived_cl946]) ).
thf(zip_derived_cl975,plain,
( ( dsetconstr @ ( setunion @ '#sk5' )
@ ^ [Y0: $i] :
( '#sk5'
= ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ '#sk5' ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) ),
inference(simplify,[status(thm)],[zip_derived_cl974]) ).
thf(zip_derived_cl1273,plain,
( ( ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) )
| ~ ( in @ '#sk20' @ ( setunion @ '#sk5' ) )
| ( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
!= '#sk20' ) ),
inference('sup-',[status(thm)],[zip_derived_cl850,zip_derived_cl975]) ).
thf(zip_derived_cl36_020,plain,
in @ '#sk20' @ ( setunion @ '#sk5' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl946_021,plain,
( ( '#sk103' @ ( setunion @ '#sk5' ) @ '#sk20' )
= '#sk20' ),
inference(simplify,[status(thm)],[zip_derived_cl883]) ).
thf(zip_derived_cl1278,plain,
( ( ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset )
!= ( setadjoin @ ( '#sk104' @ ( setunion @ '#sk5' ) ) @ emptyset ) )
| ( '#sk20' != '#sk20' ) ),
inference(demod,[status(thm)],[zip_derived_cl1273,zip_derived_cl36,zip_derived_cl946]) ).
thf(zip_derived_cl1279,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl1278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU655^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.h54dvJGBKg true
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 21:17:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.22/0.63 % Total configuration time : 828
% 0.22/0.63 % Estimated wc time : 1656
% 0.22/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.82 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 6.08/1.52 % Solved by lams/20_acsne_simpl.sh.
% 6.08/1.52 % done 173 iterations in 0.629s
% 6.08/1.52 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.08/1.52 % SZS output start Refutation
% See solution above
% 6.08/1.52
% 6.08/1.52
% 6.08/1.52 % Terminating...
% 6.08/1.56 % Runner terminated.
% 6.08/1.57 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------