TSTP Solution File: SEU678^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU678^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HtBqcolKUp true
% Computer : n004.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 19:16:04 EDT 2023
% Result : Theorem 49.67s 6.93s
% Output : Refutation 49.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 48
% Syntax : Number of formulae : 139 ( 32 unt; 24 typ; 0 def)
% Number of atoms : 748 ( 165 equ; 0 cnn)
% Maximal formula atoms : 45 ( 6 avg)
% Number of connectives : 2859 ( 115 ~; 108 |; 54 &;2182 @)
% ( 0 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 186 ( 186 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 24 usr; 11 con; 0-3 aty)
% ( 153 !!; 28 ??; 0 @@+; 0 @@-)
% Number of variables : 630 ( 366 ^; 257 !; 7 ?; 630 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf('#sk25_type',type,
'#sk25': $i > $i ).
thf('#sk50_type',type,
'#sk50': $i > ( $i > $o ) > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(dpsetconstr_type,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(setOfPairsIsBReln_type,type,
setOfPairsIsBReln: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $o ).
thf('#l_lift19433_type',type,
'#l_lift19433': $i > $o ).
thf('#sk29_type',type,
'#sk29': $i > ( $i > $o ) > $i > $i ).
thf('#sk16_type',type,
'#sk16': $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf('#l_lift19432_type',type,
'#l_lift19432': $i > $i > $o ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf('#sk60_type',type,
'#sk60': $i ).
thf(dpsetconstrI_type,type,
dpsetconstrI: $o ).
thf(ex1I_type,type,
ex1I: $o ).
thf(dpsetconstrERa_type,type,
dpsetconstrERa: $o ).
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('0',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('1',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('2',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('3',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'3']) ).
thf('5',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('6',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,'1','5','3']) ).
thf('7',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(dpsetconstrERa,axiom,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
thf('8',plain,
( dpsetconstrERa
= ( ! [X4: $i,X6: $i,X8: $i > $i > $o,X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X6 )
=> ( ( in @ ( kpair @ X10 @ X12 )
@ ( dpsetconstr @ X4 @ X6
@ ^ [V_1: $i,V_2: $i] : ( X8 @ V_1 @ V_2 ) ) )
=> ( X8 @ X10 @ X12 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setOfPairsIsBReln,axiom,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
thf('9',plain,
( setOfPairsIsBReln
= ( ! [X4: $i,X6: $i,X8: $i > $i > $o] :
( breln @ X4 @ X6
@ ( dpsetconstr @ X4 @ X6
@ ^ [V_1: $i,V_2: $i] : ( X8 @ V_1 @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(dpsetconstrI,axiom,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
thf('10',plain,
( dpsetconstrI
= ( ! [X4: $i,X6: $i,X8: $i > $i > $o,X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X6 )
=> ( ( X8 @ X10 @ X12 )
=> ( in @ ( kpair @ X10 @ X12 )
@ ( dpsetconstr @ X4 @ X6
@ ^ [V_1: $i,V_2: $i] : ( X8 @ V_1 @ V_2 ) ) ) ) ) ) ) ),
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('11',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(lamProp,conjecture,
( ex1I
=> ( dpsetconstrI
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ) ) ) ).
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,X18: $i > $i > $o,X20: $i] :
( ( in @ X20 @ X14 )
=> ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ( ( X18 @ X20 @ X22 )
=> ( in @ ( kpair @ X20 @ X22 )
@ ( dpsetconstr @ X14 @ X16
@ ^ [V_3: $i,V_4: $i] : ( X18 @ V_3 @ V_4 ) ) ) ) ) )
=> ( ! [X24: $i,X26: $i,X28: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X24 @ X26
@ ^ [V_5: $i,V_6: $i] : ( X28 @ V_5 @ V_6 ) )
@ ( cartprod @ X24 @ X26 ) )
=> ( ! [X30: $i,X32: $i,X34: $i > $i > $o,X36: $i] :
( ( in @ X36 @ X30 )
=> ! [X38: $i] :
( ( in @ X38 @ X32 )
=> ( ( in @ ( kpair @ X36 @ X38 )
@ ( dpsetconstr @ X30 @ X32
@ ^ [V_7: $i,V_8: $i] : ( X34 @ V_7 @ V_8 ) ) )
=> ( X34 @ X36 @ X38 ) ) ) )
=> ! [X40: $i,X42: $i,X44: $i > $i] :
( ! [X46: $i] :
( ( in @ X46 @ X40 )
=> ( in @ ( X44 @ X46 ) @ X42 ) )
=> ( ! [X48: $i] :
( ( in @ X48 @ X40 )
=> ? [X50: $i] :
( ( in @ X50
@ ( dsetconstr @ X42
@ ^ [V_14: $i] :
( in @ ( kpair @ X48 @ V_14 )
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_15: $i,V_16: $i] :
( ( X44 @ V_15 )
= V_16 ) ) ) ) )
& ( ( dsetconstr @ X42
@ ^ [V_11: $i] :
( in @ ( kpair @ X48 @ V_11 )
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_12: $i,V_13: $i] :
( ( X44 @ V_12 )
= V_13 ) ) ) )
= ( setadjoin @ X50 @ emptyset ) ) ) )
& ( subset
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_9: $i,V_10: $i] :
( ( X44 @ V_9 )
= V_10 ) )
@ ( cartprod @ X40 @ X42 ) ) ) ) ) ) ) ) ).
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,X18: $i > $i > $o,X20: $i] :
( ( in @ X20 @ X14 )
=> ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ( ( X18 @ X20 @ X22 )
=> ( in @ ( kpair @ X20 @ X22 )
@ ( dpsetconstr @ X14 @ X16
@ ^ [V_3: $i,V_4: $i] : ( X18 @ V_3 @ V_4 ) ) ) ) ) )
=> ( ! [X24: $i,X26: $i,X28: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X24 @ X26
@ ^ [V_5: $i,V_6: $i] : ( X28 @ V_5 @ V_6 ) )
@ ( cartprod @ X24 @ X26 ) )
=> ( ! [X30: $i,X32: $i,X34: $i > $i > $o,X36: $i] :
( ( in @ X36 @ X30 )
=> ! [X38: $i] :
( ( in @ X38 @ X32 )
=> ( ( in @ ( kpair @ X36 @ X38 )
@ ( dpsetconstr @ X30 @ X32
@ ^ [V_7: $i,V_8: $i] : ( X34 @ V_7 @ V_8 ) ) )
=> ( X34 @ X36 @ X38 ) ) ) )
=> ! [X40: $i,X42: $i,X44: $i > $i] :
( ! [X46: $i] :
( ( in @ X46 @ X40 )
=> ( in @ ( X44 @ X46 ) @ X42 ) )
=> ( ! [X48: $i] :
( ( in @ X48 @ X40 )
=> ? [X50: $i] :
( ( in @ X50
@ ( dsetconstr @ X42
@ ^ [V_14: $i] :
( in @ ( kpair @ X48 @ V_14 )
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_15: $i,V_16: $i] :
( ( X44 @ V_15 )
= V_16 ) ) ) ) )
& ( ( dsetconstr @ X42
@ ^ [V_11: $i] :
( in @ ( kpair @ X48 @ V_11 )
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_12: $i,V_13: $i] :
( ( X44 @ V_12 )
= V_13 ) ) ) )
= ( setadjoin @ X50 @ emptyset ) ) ) )
& ( subset
@ ( dpsetconstr @ X40 @ X42
@ ^ [V_9: $i,V_10: $i] :
( ( X44 @ V_9 )
= V_10 ) )
@ ( cartprod @ X40 @ X42 ) ) ) ) ) ) ) ),
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] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y2 @ Y3 @ Y4 ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y5: $i,Y6: $i] : ( Y2 @ Y5 @ Y6 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i,Y7: $i] :
( ( Y2 @ Y6 )
= Y7 ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i,Y7: $i] :
( ( Y2 @ Y6 )
= Y7 ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i,Y4: $i] :
( ( Y2 @ Y3 )
= Y4 ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
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] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] :
( $i
= ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] :
( $i
= ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] :
( $i
= ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] :
( $i
= ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl15,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( Y2 @ Y3 ) @ Y1 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] :
( in @ ( kpair @ Y3 @ Y5 )
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y6: $i] :
( $i
= ( Y2 @ Y6 ) ) ) ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ Y0 @ Y1
@ ^ [Y3: $i] :
( $i
= ( Y2 @ Y3 ) ) )
@ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl20,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk8' )
=> ( in @ ( Y1 @ Y2 ) @ Y0 ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk8' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ '#sk8' @ Y0
@ ^ [Y5: $i] :
( $i
= ( Y1 @ Y5 ) ) ) ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( in @ ( kpair @ Y2 @ Y4 )
@ ( dpsetconstr @ '#sk8' @ Y0
@ ^ [Y5: $i] :
( $i
= ( Y1 @ Y5 ) ) ) ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ '#sk8' @ Y0
@ ^ [Y2: $i] :
( $i
= ( Y1 @ Y2 ) ) )
@ ( cartprod @ '#sk8' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl25,plain,
~ ( !!
@ ^ [Y0: $i > $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk8' )
=> ( in @ ( Y0 @ Y1 ) @ '#sk16' ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk8' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk16'
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y4: $i] :
( $i
= ( Y0 @ Y4 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y3: $i] :
( in @ ( kpair @ Y1 @ Y3 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y4: $i] :
( $i
= ( Y0 @ Y4 ) ) ) ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( Y0 @ Y1 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk8' )
=> ( in @ ( '#sk25' @ Y0 ) @ '#sk16' ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk8' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl33,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk8' )
=> ( in @ ( '#sk25' @ Y0 ) @ '#sk16' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl39,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk8' )
=> ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl46,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk8' )
| ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
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_cl11,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( X4 @ X6 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( Y0 = X6 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( ( X4 @ X6 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( Y0 = X6 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( X4 @ X6 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( Y0 = X6 ) ) ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ Y0 )
=> ( Y0 = X6 ) ) ) )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
=> ( ( '#sk29' @ X2 @ X4 @ X6 )
= X6 ) ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
=> ( ( '#sk29' @ X2 @ X4 @ X6 )
= X6 ) )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 )
| ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
| ( ( '#sk29' @ X2 @ X4 @ X6 )
!= X6 )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl34,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk8' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl40,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk8' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y2: $i] :
( in @ ( kpair @ Y0 @ Y2 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y3: $i] :
( $i
= ( '#sk25' @ Y3 ) ) ) ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl47,plain,
( ~ ( ( in @ '#sk60' @ '#sk8' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk16'
@ ^ [Y1: $i] :
( in @ ( kpair @ '#sk60' @ Y1 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y2: $i] :
( $i
= ( '#sk25' @ Y2 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y1: $i] :
( in @ ( kpair @ '#sk60' @ Y1 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y2: $i] :
( $i
= ( '#sk25' @ Y2 ) ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl55,plain,
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk16'
@ ^ [Y1: $i] :
( in @ ( kpair @ '#sk60' @ Y1 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y2: $i] :
( $i
= ( '#sk25' @ Y2 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y1: $i] :
( in @ ( kpair @ '#sk60' @ Y1 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y2: $i] :
( $i
= ( '#sk25' @ Y2 ) ) ) ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ~ ( ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
& ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
= ( setadjoin @ X2 @ emptyset ) ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
| ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl66,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
| ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] : ( subset @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) @ ( cartprod @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ Y0 @ Y1 ) @ ( cartprod @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ X4 @ Y0 ) @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ X4 @ X6 ) @ ( cartprod @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl68,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
| ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl23]) ).
thf(zip_derived_cl68_001,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
| ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl23]) ).
thf(zip_derived_cl9095,plain,
! [X5: $i] :
( ( '#l_lift19433' @ X5 )
= ( in @ ( kpair @ '#sk60' @ X5 ) @ ( dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift19432' ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl68_002,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) ) )
| ( ( dsetconstr @ '#sk16'
@ ^ [Y0: $i] :
( in @ ( kpair @ '#sk60' @ Y0 )
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y1: $i] :
( $i
= ( '#sk25' @ Y1 ) ) ) ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl66,zip_derived_cl23]) ).
thf(zip_derived_cl9094,plain,
! [X3: $i,X4: $i] :
( ( '#l_lift19432' @ X3 @ X4 )
= ( ( '#sk25' @ X3 )
= X4 ) ),
define([status(thm)]) ).
thf(zip_derived_cl9095_003,plain,
! [X5: $i] :
( ( '#l_lift19433' @ X5 )
= ( in @ ( kpair @ '#sk60' @ X5 ) @ ( dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift19432' ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl9094_004,plain,
! [X3: $i,X4: $i] :
( ( '#l_lift19432' @ X3 @ X4 )
= ( ( '#sk25' @ X3 )
= X4 ) ),
define([status(thm)]) ).
thf(zip_derived_cl9096,plain,
! [X2: $i] :
( ~ ( in @ X2 @ ( dsetconstr @ '#sk16' @ '#l_lift19433' ) )
| ( ( dsetconstr @ '#sk16' @ '#l_lift19433' )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl68,zip_derived_cl9095,zip_derived_cl9094,zip_derived_cl9095,zip_derived_cl9094]) ).
thf(zip_derived_cl46_005,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk8' )
| ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 )
| ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl280,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( in @ X0 @ '#sk8' )
| ~ ( X1 @ ( '#sk25' @ X0 ) )
| ( in @ ( '#sk29' @ '#sk16' @ X1 @ ( '#sk25' @ X0 ) ) @ '#sk16' )
| ( ( dsetconstr @ '#sk16' @ X1 )
= ( setadjoin @ ( '#sk50' @ '#sk16' @ X1 ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl56]) ).
thf(zip_derived_cl54,plain,
( ( in @ '#sk60' @ '#sk8' )
| ~ ( subset
@ ( dpsetconstr @ '#sk8' @ '#sk16'
@ ^ [Y0: $i] :
( $i
= ( '#sk25' @ Y0 ) ) )
@ ( cartprod @ '#sk8' @ '#sk16' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl23_006,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o] : ( subset @ ( dpsetconstr @ X2 @ X4 @ X6 ) @ ( cartprod @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl67,plain,
in @ '#sk60' @ '#sk8',
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl23]) ).
thf(zip_derived_cl46_007,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk8' )
| ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
| ( in @ ( '#sk29' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl163,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( in @ X0 @ '#sk8' )
| ~ ( X1 @ ( '#sk25' @ X0 ) )
| ( in @ ( '#sk29' @ '#sk16' @ X1 @ ( '#sk25' @ X0 ) ) @ '#sk16' )
| ( in @ ( '#sk50' @ '#sk16' @ X1 ) @ ( dsetconstr @ '#sk16' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl48]) ).
thf(zip_derived_cl46_008,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk8' )
| ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( X4 @ X6 )
| ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ ( '#sk50' @ X2 @ X4 ) @ ( dsetconstr @ X2 @ X4 ) )
| ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl428,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( in @ X0 @ '#sk8' )
| ~ ( X1 @ ( '#sk25' @ X0 ) )
| ( X1 @ ( '#sk29' @ '#sk16' @ X1 @ ( '#sk25' @ X0 ) ) )
| ( in @ ( '#sk50' @ '#sk16' @ X1 ) @ ( dsetconstr @ '#sk16' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl57]) ).
thf(zip_derived_cl9094_009,plain,
! [X3: $i,X4: $i] :
( ( '#l_lift19432' @ X3 @ X4 )
= ( ( '#sk25' @ X3 )
= X4 ) ),
define([status(thm)]) ).
thf(zip_derived_cl9095_010,plain,
! [X5: $i] :
( ( '#l_lift19433' @ X5 )
= ( in @ ( kpair @ '#sk60' @ X5 ) @ ( dpsetconstr @ '#sk8' @ '#sk16' @ '#l_lift19432' ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl46_011,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk8' )
| ( in @ ( '#sk25' @ X2 ) @ '#sk16' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ ( '#sk50' @ X2 @ X4 ) @ emptyset ) )
| ( X4 @ ( '#sk29' @ X2 @ X4 @ X6 ) )
| ~ ( X4 @ X6 )
| ~ ( in @ X6 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl513,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( in @ X0 @ '#sk8' )
| ~ ( X1 @ ( '#sk25' @ X0 ) )
| ( X1 @ ( '#sk29' @ '#sk16' @ X1 @ ( '#sk25' @ X0 ) ) )
| ( ( dsetconstr @ '#sk16' @ X1 )
= ( setadjoin @ ( '#sk50' @ '#sk16' @ X1 ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl63]) ).
thf(zip_derived_cl67_012,plain,
in @ '#sk60' @ '#sk8',
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl23]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ X2 @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X4 @ Y0 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
=> ( X6 @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i] :
( ( in @ X8 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X8 @ Y0 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
=> ( X6 @ X8 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X8 @ Y0 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
=> ( X6 @ X8 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
=> ( X6 @ X8 @ X10 ) ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X4 )
| ( ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
=> ( X6 @ X8 @ X10 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ~ ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
| ( X6 @ X8 @ X10 )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl92,plain,
! [X0: $i,X1: $i,X2: $i > $i > $o] :
( ~ ( in @ X1 @ X0 )
| ( X2 @ '#sk60' @ X1 )
| ~ ( in @ ( kpair @ '#sk60' @ X1 ) @ ( dpsetconstr @ '#sk8' @ X0 @ X2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl67,zip_derived_cl61]) ).
thf(zip_derived_cl67_013,plain,
in @ '#sk60' @ '#sk8',
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl23]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i > $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( Y2 @ Y3 @ Y4 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ ( dpsetconstr @ Y0 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 @ Y3 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ ( dpsetconstr @ X2 @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i > $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
=> ( ( Y0 @ Y1 @ Y2 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ ( dpsetconstr @ X2 @ X4 @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( X6 @ Y0 @ Y1 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i] :
( ( in @ X8 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( X6 @ X8 @ Y0 )
=> ( in @ ( kpair @ X8 @ Y0 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( X6 @ X8 @ Y0 )
=> ( in @ ( kpair @ X8 @ Y0 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ( ( in @ X10 @ X4 )
=> ( ( X6 @ X8 @ X10 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) ) ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X4 )
| ( ( X6 @ X8 @ X10 )
=> ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i,X6: $i > $i > $o,X8: $i,X10: $i] :
( ~ ( X6 @ X8 @ X10 )
| ( in @ ( kpair @ X8 @ X10 ) @ ( dpsetconstr @ X2 @ X4 @ X6 ) )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl96,plain,
! [X0: $i,X1: $i,X2: $i > $i > $o] :
( ~ ( in @ X1 @ X0 )
| ( in @ ( kpair @ '#sk60' @ X1 ) @ ( dpsetconstr @ '#sk8' @ X0 @ X2 ) )
| ~ ( X2 @ '#sk60' @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl67,zip_derived_cl44]) ).
thf(zip_derived_cl9099,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl46,zip_derived_cl64,zip_derived_cl59,zip_derived_cl9096,zip_derived_cl280,zip_derived_cl67,zip_derived_cl163,zip_derived_cl428,zip_derived_cl9094,zip_derived_cl9095,zip_derived_cl513,zip_derived_cl92,zip_derived_cl96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU678^2 : TPTP v8.1.2. Released v3.7.0.
% 0.13/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HtBqcolKUp true
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 22:52:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in HO mode
% 0.19/0.64 % Total configuration time : 828
% 0.19/0.64 % Estimated wc time : 1656
% 0.19/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.19/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.00/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.00/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.00/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.00/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.00/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.00/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.00/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 49.67/6.93 % Solved by lams/20_acsne_simpl.sh.
% 49.67/6.93 % done 493 iterations in 6.112s
% 49.67/6.93 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 49.67/6.93 % SZS output start Refutation
% See solution above
% 49.67/6.93
% 49.67/6.93
% 49.67/6.93 % Terminating...
% 49.67/6.97 % Runner terminated.
% 49.67/6.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------