TSTP Solution File: SEU686^2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU686^2 : 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.vMXI4feYTF true
% Computer : n025.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 19:16:12 EDT 2023
% Result : Theorem 1.45s 0.99s
% Output : Refutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 38
% Syntax : Number of formulae : 155 ( 36 unt; 22 typ; 0 def)
% Number of atoms : 949 ( 149 equ; 0 cnn)
% Maximal formula atoms : 52 ( 7 avg)
% Number of connectives : 3751 ( 171 ~; 162 |; 90 &;2874 @)
% ( 0 <=>; 256 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 12 con; 0-4 aty)
% ( 157 !!; 41 ??; 0 @@+; 0 @@-)
% Number of variables : 623 ( 354 ^; 258 !; 11 ?; 623 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk11_type',type,
'#sk11': $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf('#sk35_type',type,
'#sk35': $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk25_type',type,
'#sk25': $i ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf('#sk12_type',type,
'#sk12': $i > $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf('#sk32_type',type,
'#sk32': $i ).
thf(ex1E2_type,type,
ex1E2: $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(app_type,type,
app: $o ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(funcGraphProp1,axiom,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
thf('0',plain,
( funcGraphProp1
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( kpair @ X10 @ ( ap @ X4 @ X6 @ X8 @ X10 ) ) @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(ex1E2,axiom,
( ex1E2
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ) ).
thf('1',plain,
( ex1E2
= ( ! [X4: $i,X6: $i > $o] :
( ( ex1 @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( X6 @ X8 )
=> ( ( X6 @ X10 )
=> ( X8 = X10 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(app,axiom,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
thf('2',plain,
( app
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( ap @ X4 @ X6 @ X8 @ X10 ) @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(func,axiom,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
thf(breln,axiom,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf('3',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('4',plain,
( breln
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(ex1,axiom,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
thf(singleton,axiom,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ) ).
thf('5',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('6',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('7',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'6']) ).
thf('8',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('9',plain,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[func,'4','8','6']) ).
thf('10',plain,
( func
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( ( breln @ V_1 @ V_2 @ V_3 )
& ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( ex1 @ V_2
@ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
define([status(thm)]) ).
thf(funcGraphProp2,conjecture,
( app
=> ( ex1E2
=> ( funcGraphProp1
=> ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i,X8: $i] :
( ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ? [X12: $i] :
( ( in @ X12
@ ( dsetconstr @ X6
@ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) )
& ( ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
= ( setadjoin @ X12 @ emptyset ) ) ) )
& ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) )
=> ( ! [X16: $i,X18: $i > $o] :
( ? [X20: $i] :
( ( in @ X20
@ ( dsetconstr @ X16
@ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) )
= ( setadjoin @ X20 @ emptyset ) ) )
=> ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ! [X24: $i] :
( ( in @ X24 @ X16 )
=> ( ( X18 @ X22 )
=> ( ( X18 @ X24 )
=> ( X22 = X24 ) ) ) ) ) )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( ! [X32: $i] :
( ( in @ X32 @ X26 )
=> ? [X34: $i] :
( ( in @ X34
@ ( dsetconstr @ X28
@ ^ [V_6: $i] : ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) )
& ( ( dsetconstr @ X28
@ ^ [V_5: $i] : ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) )
= ( setadjoin @ X34 @ emptyset ) ) ) )
& ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) )
=> ! [X36: $i] :
( ( in @ X36 @ X26 )
=> ( in @ ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) )
=> ! [X38: $i,X40: $i,X42: $i] :
( ( ! [X44: $i] :
( ( in @ X44 @ X38 )
=> ? [X46: $i] :
( ( in @ X46
@ ( dsetconstr @ X40
@ ^ [V_8: $i] : ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) )
& ( ( dsetconstr @ X40
@ ^ [V_7: $i] : ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) )
= ( setadjoin @ X46 @ emptyset ) ) ) )
& ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) )
=> ! [X48: $i] :
( ( in @ X48 @ X38 )
=> ! [X50: $i] :
( ( in @ X50 @ X40 )
=> ( ( in @ ( kpair @ X48 @ X50 ) @ X42 )
=> ( ( ap @ X38 @ X40 @ X42 @ X48 )
= X50 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i,X8: $i] :
( ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ? [X12: $i] :
( ( in @ X12
@ ( dsetconstr @ X6
@ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) )
& ( ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
= ( setadjoin @ X12 @ emptyset ) ) ) )
& ( subset @ X8 @ ( cartprod @ X4 @ X6 ) ) )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( in @ ( ap @ X4 @ X6 @ X8 @ X14 ) @ X6 ) ) )
=> ( ! [X16: $i,X18: $i > $o] :
( ? [X20: $i] :
( ( in @ X20
@ ( dsetconstr @ X16
@ ^ [V_4: $i] : ( X18 @ V_4 ) ) )
& ( ( dsetconstr @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) )
= ( setadjoin @ X20 @ emptyset ) ) )
=> ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ! [X24: $i] :
( ( in @ X24 @ X16 )
=> ( ( X18 @ X22 )
=> ( ( X18 @ X24 )
=> ( X22 = X24 ) ) ) ) ) )
=> ( ! [X26: $i,X28: $i,X30: $i] :
( ( ! [X32: $i] :
( ( in @ X32 @ X26 )
=> ? [X34: $i] :
( ( in @ X34
@ ( dsetconstr @ X28
@ ^ [V_6: $i] : ( in @ ( kpair @ X32 @ V_6 ) @ X30 ) ) )
& ( ( dsetconstr @ X28
@ ^ [V_5: $i] : ( in @ ( kpair @ X32 @ V_5 ) @ X30 ) )
= ( setadjoin @ X34 @ emptyset ) ) ) )
& ( subset @ X30 @ ( cartprod @ X26 @ X28 ) ) )
=> ! [X36: $i] :
( ( in @ X36 @ X26 )
=> ( in @ ( kpair @ X36 @ ( ap @ X26 @ X28 @ X30 @ X36 ) ) @ X30 ) ) )
=> ! [X38: $i,X40: $i,X42: $i] :
( ( ! [X44: $i] :
( ( in @ X44 @ X38 )
=> ? [X46: $i] :
( ( in @ X46
@ ( dsetconstr @ X40
@ ^ [V_8: $i] : ( in @ ( kpair @ X44 @ V_8 ) @ X42 ) ) )
& ( ( dsetconstr @ X40
@ ^ [V_7: $i] : ( in @ ( kpair @ X44 @ V_7 ) @ X42 ) )
= ( setadjoin @ X46 @ emptyset ) ) ) )
& ( subset @ X42 @ ( cartprod @ X38 @ X40 ) ) )
=> ! [X48: $i] :
( ( in @ X48 @ X38 )
=> ! [X50: $i] :
( ( in @ X50 @ X40 )
=> ( ( in @ ( kpair @ X48 @ X50 ) @ X42 )
=> ( ( ap @ X38 @ X40 @ X42 @ X48 )
= X50 ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( dsetconstr @ Y0 @ Y1 )
= ( setadjoin @ Y2 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( dsetconstr @ Y0 @ Y1 )
= ( setadjoin @ Y2 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl14,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ '#sk1' @ Y0 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl18,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk6'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk6' ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk6' )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ '#sk1' @ '#sk6' @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl22,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk6' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl34,plain,
subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl33,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk11' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl40,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk11' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl55,plain,
! [X2: $i] :
( ( ( in @ ( '#sk35' @ X2 )
@ ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
& ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
= ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ( in @ ( '#sk35' @ X2 )
@ ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( in @ ( ap @ X2 @ Y0 @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X4
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ Y0 @ Y1 ) @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
= ( setadjoin @ X8 @ emptyset ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( in @ X10 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ X10 ) @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X2 )
| ( in @ ( ap @ X2 @ X4 @ X6 @ X10 ) @ X4 )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl113,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
| ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ Y0 ) @ '#sk11' ) )
!= ( setadjoin @ ( '#sk35' @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) ) @ emptyset ) )
| ( in @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) @ '#sk6' )
| ~ ( in @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl58]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
= ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl69,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
= ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl125,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) @ '#sk6' )
| ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
| ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl113,zip_derived_cl69]) ).
thf(zip_derived_cl126,plain,
! [X0: $i] :
( ~ ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl125]) ).
thf(zip_derived_cl34_001,plain,
subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ Y0 ) @ X4 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( in @ ( ap @ X2 @ X4 @ X6 @ X8 ) @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( in @ ( ap @ X2 @ X4 @ X6 @ X8 ) @ X4 )
| ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl96,plain,
! [X0: $i] :
( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl43]) ).
thf(zip_derived_cl128,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl126,zip_derived_cl96]) ).
thf(zip_derived_cl27,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk6' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ Y0 )
= Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,plain,
~ ( ( in @ '#sk25' @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk6' )
=> ( ( in @ ( kpair @ '#sk25' @ Y0 ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl42,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk6' )
=> ( ( in @ ( kpair @ '#sk25' @ Y0 ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl49,plain,
~ ( ( in @ '#sk32' @ '#sk6' )
=> ( ( in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl57,plain,
~ ( ( in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11' )
=> ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl64,plain,
in @ ( kpair @ '#sk25' @ '#sk32' ) @ '#sk11',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl62_002,plain,
! [X2: $i] :
( ( in @ ( '#sk35' @ X2 )
@ ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
& ( ( dsetconstr @ Y0 @ Y1 )
= ( setadjoin @ Y2 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
& ( ( dsetconstr @ X2 @ Y0 )
= ( setadjoin @ Y1 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i > $o] :
( ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( X4 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i > $o] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( X4 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
& ( ( dsetconstr @ X2 @ X4 )
= ( setadjoin @ X6 @ emptyset ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( X4 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( X4 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( X4 @ Y0 )
=> ( ( X4 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ X8 )
=> ( ( X4 @ Y0 )
=> ( X8 = Y0 ) ) ) ) ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( X4 @ X8 )
=> ( ( X4 @ Y0 )
=> ( X8 = Y0 ) ) ) ) )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
( ( ( in @ X10 @ X2 )
=> ( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X8 = X10 ) ) ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X2 )
| ( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X8 = X10 ) ) )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
( ~ ( X4 @ X8 )
| ( ( X4 @ X10 )
=> ( X8 = X10 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X10 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
( ~ ( X4 @ X10 )
| ( X8 = X10 )
| ~ ( in @ X10 @ X2 )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ~ ( X4 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i > $o,X6: $i,X8: $i,X10: $i] :
( ~ ( X4 @ X10 )
| ( X8 = X10 )
| ~ ( in @ X10 @ X2 )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( ( dsetconstr @ X2 @ X4 )
!= ( setadjoin @ X6 @ emptyset ) )
| ~ ( X4 @ X8 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl81,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ~ ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' )
@ X1 )
| ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' ) )
!= ( setadjoin @ ( '#sk35' @ X0 ) @ emptyset ) )
| ~ ( in @ X1 @ '#sk6' )
| ~ ( in @ X2 @ '#sk6' )
| ( X1 = X2 )
| ~ ( ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' )
@ X2 ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl71]) ).
thf(zip_derived_cl95,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ ( kpair @ X0 @ X1 ) @ '#sk11' )
| ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X0 @ Y0 ) @ '#sk11' ) )
!= ( setadjoin @ ( '#sk35' @ X0 ) @ emptyset ) )
| ~ ( in @ X1 @ '#sk6' )
| ~ ( in @ X2 @ '#sk6' )
| ( X1 = X2 )
| ~ ( in @ ( kpair @ X0 @ X2 ) @ '#sk11' ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl69_003,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
= ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl130,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( kpair @ X0 @ X2 ) @ '#sk11' )
| ( X1 = X2 )
| ~ ( in @ X2 @ '#sk6' )
| ~ ( in @ X1 @ '#sk6' )
| ~ ( in @ ( kpair @ X0 @ X1 ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl95,zip_derived_cl69]) ).
thf(zip_derived_cl131,plain,
! [X0: $i] :
( ~ ( in @ '#sk25' @ '#sk1' )
| ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk6' )
| ~ ( in @ '#sk32' @ '#sk6' )
| ( X0 = '#sk32' ) ),
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl130]) ).
thf(zip_derived_cl41,plain,
in @ '#sk25' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl56,plain,
in @ '#sk32' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl138,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk6' )
| ( X0 = '#sk32' ) ),
inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl41,zip_derived_cl56]) ).
thf(zip_derived_cl34_004,plain,
subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl62_005,plain,
! [X2: $i] :
( ( in @ ( '#sk35' @ X2 )
@ ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( in @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( in @ ( kpair @ Y2 @ ( ap @ X2 @ Y0 @ Y1 @ Y2 ) ) @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ X4
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( in @ ( kpair @ Y1 @ ( ap @ X2 @ X4 @ Y0 @ Y1 ) ) @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X6 ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
= ( setadjoin @ X8 @ emptyset ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( in @ X10 @ X2 )
=> ( in @ ( kpair @ X10 @ ( ap @ X2 @ X4 @ X6 @ X10 ) ) @ X6 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X2 )
| ( in @ ( kpair @ X10 @ ( ap @ X2 @ X4 @ X6 @ X10 ) ) @ X6 )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl144,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
| ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ Y0 ) @ '#sk11' ) )
!= ( setadjoin @ ( '#sk35' @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) ) @ emptyset ) )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) ) @ '#sk11' )
| ~ ( in @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl72]) ).
thf(zip_derived_cl69_006,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk6'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk11' ) )
= ( setadjoin @ ( '#sk35' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl201,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk6' @ '#sk11' @ X1 ) ) @ '#sk11' )
| ~ ( subset @ '#sk11' @ ( cartprod @ X0 @ '#sk6' ) )
| ~ ( in @ ( '#sk12' @ X0 @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl144,zip_derived_cl69]) ).
thf(zip_derived_cl202,plain,
! [X0: $i] :
( ~ ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl201]) ).
thf(zip_derived_cl128_007,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl126,zip_derived_cl96]) ).
thf(zip_derived_cl34_008,plain,
subset @ '#sk11' @ ( cartprod @ '#sk1' @ '#sk6' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( in @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( in @ ( kpair @ X8 @ ( ap @ X2 @ X4 @ X6 @ X8 ) ) @ X6 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( in @ ( kpair @ X8 @ ( ap @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
| ( in @ ( '#sk12' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl98,plain,
! [X0: $i] :
( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl60]) ).
thf(zip_derived_cl138_009,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ '#sk25' @ X0 ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk6' )
| ( X0 = '#sk32' ) ),
inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl41,zip_derived_cl56]) ).
thf(zip_derived_cl148,plain,
( ~ ( in @ '#sk25' @ '#sk1' )
| ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' )
| ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl98,zip_derived_cl138]) ).
thf(zip_derived_cl41_010,plain,
in @ '#sk25' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl154,plain,
( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' )
| ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
inference(demod,[status(thm)],[zip_derived_cl148,zip_derived_cl41]) ).
thf(zip_derived_cl65,plain,
( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
!= '#sk32' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl70,plain,
( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
!= '#sk32' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl155,plain,
( ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' )
| ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl154,zip_derived_cl70]) ).
thf(zip_derived_cl166,plain,
( ~ ( in @ '#sk25' @ '#sk1' )
| ( in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl155]) ).
thf(zip_derived_cl41_011,plain,
in @ '#sk25' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl169,plain,
in @ ( '#sk12' @ '#sk1' @ '#sk6' @ '#sk11' ) @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl166,zip_derived_cl41]) ).
thf(zip_derived_cl204,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ X0 ) ) @ '#sk11' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl202,zip_derived_cl169]) ).
thf(zip_derived_cl208,plain,
( ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' )
| ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' )
| ~ ( in @ '#sk25' @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl138,zip_derived_cl204]) ).
thf(zip_derived_cl41_012,plain,
in @ '#sk25' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl212,plain,
( ( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
= '#sk32' )
| ~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ) ),
inference(demod,[status(thm)],[zip_derived_cl208,zip_derived_cl41]) ).
thf(zip_derived_cl70_013,plain,
( ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' )
!= '#sk32' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl213,plain,
~ ( in @ ( ap @ '#sk1' @ '#sk6' @ '#sk11' @ '#sk25' ) @ '#sk6' ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl212,zip_derived_cl70]) ).
thf(zip_derived_cl223,plain,
~ ( in @ '#sk25' @ '#sk1' ),
inference('sup-',[status(thm)],[zip_derived_cl128,zip_derived_cl213]) ).
thf(zip_derived_cl41_014,plain,
in @ '#sk25' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl227,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl223,zip_derived_cl41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU686^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.vMXI4feYTF true
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 14:27:50 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/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
% 0.20/0.68 % Total configuration time : 828
% 0.20/0.68 % Estimated wc time : 1656
% 0.20/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.27/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.27/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.45/0.99 % Solved by lams/35_full_unif4.sh.
% 1.45/0.99 % done 45 iterations in 0.144s
% 1.45/0.99 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.45/0.99 % SZS output start Refutation
% See solution above
% 1.45/0.99
% 1.45/0.99
% 1.45/0.99 % Terminating...
% 1.66/1.08 % Runner terminated.
% 1.76/1.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------