%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU687^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.aq1rYNDiXn true
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:55:46 PM UTC 2025
% Result : Theorem 3.43s 1.67s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of formulae : 138 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 1037 ( 145 equ; 0 cnn)
% Maximal formula atoms : 56 ( 7 avg)
% Number of connectives : 4226 ( 181 ~; 181 |; 96 &;3319 @)
% ( 0 <=>; 258 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 23 usr; 12 con; 0-4 aty)
% ( 150 !!; 41 ??; 0 @@+; 0 @@-)
% Number of variables : 636 ( 362 ^; 263 !; 11 ?; 636 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ap_type,type,
ap: $i > $i > $i > $i > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(funcGraphProp2_type,type,
funcGraphProp2: $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk6_type',type,
'#sk6': $i > $i ).
thf('#sk8_type',type,
'#sk8': $i > $i ).
thf('#sk9_type',type,
'#sk9': $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i > $i ).
thf('#sk7_type',type,
'#sk7': $i ).
thf(funcGraphProp1_type,type,
funcGraphProp1: $o ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(funcGraphProp2,axiom,
( funcGraphProp2
= ( ! [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('0',plain,
( funcGraphProp2
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X6 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X8 )
=> ( ( ap @ X4 @ X6 @ X8 @ X10 )
= X12 ) ) ) ) ) ) ),
define([status(thm)]) ).
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('1',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(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('2',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('3',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('4',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('5',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'5']) ).
thf('7',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('8',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,'3','7','5']) ).
thf('9',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(funcextLem,conjecture,
( funcGraphProp1
=> ( funcGraphProp2
=> ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
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 @ ( kpair @ X14 @ ( ap @ X4 @ X6 @ X8 @ X14 ) ) @ X8 ) ) )
=> ( ! [X16: $i,X18: $i,X20: $i] :
( ( ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ X18
@ ^ [V_4: $i] : ( in @ ( kpair @ X22 @ V_4 ) @ X20 ) ) )
& ( ( dsetconstr @ X18
@ ^ [V_3: $i] : ( in @ ( kpair @ X22 @ V_3 ) @ X20 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) )
& ( subset @ X20 @ ( cartprod @ X16 @ X18 ) ) )
=> ! [X26: $i] :
( ( in @ X26 @ X16 )
=> ! [X28: $i] :
( ( in @ X28 @ X18 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X20 )
=> ( ( ap @ X16 @ X18 @ X20 @ X26 )
= X28 ) ) ) ) )
=> ! [X30: $i,X32: $i,X34: $i] :
( ( ! [X36: $i] :
( ( in @ X36 @ X30 )
=> ? [X38: $i] :
( ( in @ X38
@ ( dsetconstr @ X32
@ ^ [V_6: $i] : ( in @ ( kpair @ X36 @ V_6 ) @ X34 ) ) )
& ( ( dsetconstr @ X32
@ ^ [V_5: $i] : ( in @ ( kpair @ X36 @ V_5 ) @ X34 ) )
= ( setadjoin @ X38 @ emptyset ) ) ) )
& ( subset @ X34 @ ( cartprod @ X30 @ X32 ) ) )
=> ! [X40: $i] :
( ( ! [X42: $i] :
( ( in @ X42 @ X30 )
=> ? [X44: $i] :
( ( in @ X44
@ ( dsetconstr @ X32
@ ^ [V_8: $i] : ( in @ ( kpair @ X42 @ V_8 ) @ X40 ) ) )
& ( ( dsetconstr @ X32
@ ^ [V_7: $i] : ( in @ ( kpair @ X42 @ V_7 ) @ X40 ) )
= ( setadjoin @ X44 @ emptyset ) ) ) )
& ( subset @ X40 @ ( cartprod @ X30 @ X32 ) ) )
=> ( ! [X46: $i] :
( ( in @ X46 @ X30 )
=> ( ( ap @ X30 @ X32 @ X34 @ X46 )
= ( ap @ X30 @ X32 @ X40 @ X46 ) ) )
=> ! [X48: $i] :
( ( in @ X48 @ X30 )
=> ! [X50: $i] :
( ( in @ X50 @ X32 )
=> ( ( in @ ( kpair @ X48 @ X50 ) @ X40 )
=> ( in @ ( kpair @ X48 @ X50 ) @ X34 ) ) ) ) ) ) ) ) ) ).
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 @ ( kpair @ X14 @ ( ap @ X4 @ X6 @ X8 @ X14 ) ) @ X8 ) ) )
=> ( ! [X16: $i,X18: $i,X20: $i] :
( ( ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ? [X24: $i] :
( ( in @ X24
@ ( dsetconstr @ X18
@ ^ [V_4: $i] : ( in @ ( kpair @ X22 @ V_4 ) @ X20 ) ) )
& ( ( dsetconstr @ X18
@ ^ [V_3: $i] : ( in @ ( kpair @ X22 @ V_3 ) @ X20 ) )
= ( setadjoin @ X24 @ emptyset ) ) ) )
& ( subset @ X20 @ ( cartprod @ X16 @ X18 ) ) )
=> ! [X26: $i] :
( ( in @ X26 @ X16 )
=> ! [X28: $i] :
( ( in @ X28 @ X18 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X20 )
=> ( ( ap @ X16 @ X18 @ X20 @ X26 )
= X28 ) ) ) ) )
=> ! [X30: $i,X32: $i,X34: $i] :
( ( ! [X36: $i] :
( ( in @ X36 @ X30 )
=> ? [X38: $i] :
( ( in @ X38
@ ( dsetconstr @ X32
@ ^ [V_6: $i] : ( in @ ( kpair @ X36 @ V_6 ) @ X34 ) ) )
& ( ( dsetconstr @ X32
@ ^ [V_5: $i] : ( in @ ( kpair @ X36 @ V_5 ) @ X34 ) )
= ( setadjoin @ X38 @ emptyset ) ) ) )
& ( subset @ X34 @ ( cartprod @ X30 @ X32 ) ) )
=> ! [X40: $i] :
( ( ! [X42: $i] :
( ( in @ X42 @ X30 )
=> ? [X44: $i] :
( ( in @ X44
@ ( dsetconstr @ X32
@ ^ [V_8: $i] : ( in @ ( kpair @ X42 @ V_8 ) @ X40 ) ) )
& ( ( dsetconstr @ X32
@ ^ [V_7: $i] : ( in @ ( kpair @ X42 @ V_7 ) @ X40 ) )
= ( setadjoin @ X44 @ emptyset ) ) ) )
& ( subset @ X40 @ ( cartprod @ X30 @ X32 ) ) )
=> ( ! [X46: $i] :
( ( in @ X46 @ X30 )
=> ( ( ap @ X30 @ X32 @ X34 @ X46 )
= ( ap @ X30 @ X32 @ X40 @ X46 ) ) )
=> ! [X48: $i] :
( ( in @ X48 @ X30 )
=> ! [X50: $i] :
( ( in @ X50 @ X32 )
=> ( ( in @ ( kpair @ X48 @ X50 ) @ X40 )
=> ( in @ ( kpair @ X48 @ X50 ) @ X34 ) ) ) ) ) ) ) ) ),
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 @ ( 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 ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [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] :
( ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= ( ap @ Y0 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
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 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [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] :
( ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= ( ap @ Y0 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,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] :
( ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y4 )
= ( ap @ Y0 @ Y1 @ Y3 @ Y4 ) ) ) )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,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] :
( ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk1' )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ '#sk1' @ Y0 ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk1' )
=> ( ( ap @ '#sk1' @ Y0 @ Y1 @ Y3 )
= ( ap @ '#sk1' @ Y0 @ Y2 @ Y3 ) ) ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk1' )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ '#sk2'
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ Y0 @ Y2 )
= ( ap @ '#sk1' @ '#sk2' @ Y1 @ Y2 ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk2' )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y1 )
= ( ap @ '#sk1' @ '#sk2' @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk2' )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ '#sk3' ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl18,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y1 )
= ( ap @ '#sk1' @ '#sk2' @ Y0 @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk2' )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ '#sk3' ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl23,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y0 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk2' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk5' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl29,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y0 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ Y0 ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk2' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk5' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl38,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk2' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk5' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl46,plain,
~ ( ( in @ '#sk7' @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk2' )
=> ( ( in @ ( kpair @ '#sk7' @ Y0 ) @ '#sk5' )
=> ( in @ ( kpair @ '#sk7' @ Y0 ) @ '#sk3' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl56,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk2' )
=> ( ( in @ ( kpair @ '#sk7' @ Y0 ) @ '#sk5' )
=> ( in @ ( kpair @ '#sk7' @ Y0 ) @ '#sk3' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl64,plain,
~ ( ( in @ '#sk9' @ '#sk2' )
=> ( ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk5' )
=> ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl70,plain,
~ ( ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk5' )
=> ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl75,plain,
~ ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl74,plain,
in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl55,plain,
in @ '#sk7' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl74_001,plain,
in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl55_002,plain,
in @ '#sk7' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl28,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl36,plain,
subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl4,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_cl2]) ).
thf(zip_derived_cl7,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 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ X2 @ Y0 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl10,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 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ X2 @ X4 @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl13,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 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,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 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl20,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 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X8 @ Y0 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X8 )
= Y0 ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X8 @ Y0 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X8 )
= Y0 ) ) ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X8 @ X10 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X8 )
= X10 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X4 )
| ( ( in @ ( kpair @ X8 @ X10 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X8 )
= X10 ) )
| ~ ( in @ X8 @ X2 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ ( kpair @ X8 @ X10 ) @ X6 )
| ( ( ap @ X2 @ X4 @ X6 @ X8 )
= X10 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ ( kpair @ X8 @ X10 ) @ X6 )
| ( ( ap @ X2 @ X4 @ X6 @ X8 )
= X10 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X8 @ X2 )
| ~ ( in @ X10 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl86,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk2' )
| ~ ( in @ X1 @ '#sk1' )
| ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X1 )
= X0 )
| ~ ( in @ ( kpair @ X1 @ X0 ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl36,zip_derived_cl76]) ).
thf(zip_derived_cl90,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ '#sk7' )
= X0 )
| ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl86]) ).
thf(zip_derived_cl37,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ Y0 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X2 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X2 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X2 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl63_003,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X2 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl63_004,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X2 )
= ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl17,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl21,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk3' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk3' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl34,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk3' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ( ( in @ ( '#sk6' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) )
= ( setadjoin @ ( '#sk6' @ X2 ) @ emptyset ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( in @ ( '#sk6' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
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 @ ( kpair @ Y3 @ ( ap @ Y0 @ Y1 @ Y2 @ Y3 ) ) @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,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_cl1]) ).
thf(zip_derived_cl6,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_cl3]) ).
thf(zip_derived_cl9,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_cl6]) ).
thf(zip_derived_cl12,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_cl9]) ).
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 @ ( kpair @ Y0 @ ( ap @ X2 @ X4 @ X6 @ Y0 ) ) @ X6 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ 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_cl15]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ 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_cl19]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ 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_cl25]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ 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_cl31]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ 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_cl40]) ).
thf(zip_derived_cl48,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 @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl57,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 @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl109,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk4' @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( subset @ '#sk3' @ ( cartprod @ X0 @ '#sk2' ) )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X0 @ '#sk2' @ '#sk3' ) @ Y0 ) @ '#sk3' ) )
!= ( setadjoin @ ( '#sk6' @ ( '#sk4' @ X0 @ '#sk2' @ '#sk3' ) ) @ emptyset ) )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk2' @ '#sk3' @ X1 ) ) @ '#sk3' )
| ~ ( in @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl57]) ).
thf(zip_derived_cl52,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) )
= ( setadjoin @ ( '#sk6' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) )
= ( setadjoin @ ( '#sk6' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl123,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ ( kpair @ X1 @ ( ap @ X0 @ '#sk2' @ '#sk3' @ X1 ) ) @ '#sk3' )
| ~ ( subset @ '#sk3' @ ( cartprod @ X0 @ '#sk2' ) )
| ~ ( in @ ( '#sk4' @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl109,zip_derived_cl61]) ).
thf(zip_derived_cl124,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk2' ) )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl63,zip_derived_cl123]) ).
thf(zip_derived_cl22,plain,
subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl126,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl124,zip_derived_cl22]) ).
thf(zip_derived_cl127,plain,
! [X0: $i] :
( ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl219,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl63,zip_derived_cl127]) ).
thf(zip_derived_cl225,plain,
! [X0: $i] :
( ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X0 ) ) @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl22_005,plain,
subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ 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_cl19]) ).
thf(zip_derived_cl30,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 @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( in @ ( kpair @ X8 @ ( ap @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl83,plain,
! [X0: $i] :
( ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl39]) ).
thf(zip_derived_cl444,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk3' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl225,zip_derived_cl83]) ).
thf(zip_derived_cl449,plain,
! [X0: $i] :
( ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl63,zip_derived_cl444]) ).
thf(zip_derived_cl463,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl449]) ).
thf(zip_derived_cl482,plain,
! [X0: $i] :
( ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk2' )
| ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' )
| ~ ( in @ '#sk7' @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl90,zip_derived_cl463]) ).
thf(zip_derived_cl55_006,plain,
in @ '#sk7' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl496,plain,
! [X0: $i] :
( ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk2' )
| ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl482,zip_derived_cl55]) ).
thf(zip_derived_cl545,plain,
( ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ~ ( in @ '#sk9' @ '#sk2' )
| ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl496]) ).
thf(zip_derived_cl69,plain,
in @ '#sk9' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl558,plain,
( ( in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl545,zip_derived_cl69]) ).
thf(zip_derived_cl75_007,plain,
~ ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl578,plain,
in @ ( '#sk4' @ '#sk1' @ '#sk2' @ '#sk5' ) @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl558,zip_derived_cl75]) ).
thf(zip_derived_cl35,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ( ( in @ ( '#sk8' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk8' @ X2 ) @ emptyset ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl67,plain,
! [X2: $i] :
( ( in @ ( '#sk8' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y1: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y1 ) @ X6 ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
& ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
= ( setadjoin @ X8 @ emptyset ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ Y0 )
= Y1 ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ( ( in @ X10 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X10 @ Y0 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X10 )
= Y0 ) ) ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i] :
( ~ ( in @ X10 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ X10 @ Y0 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X10 )
= Y0 ) ) ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X10 )
= X12 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ~ ( in @ X10 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( in @ X12 @ X4 )
| ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( ( ap @ X2 @ X4 @ X6 @ X10 )
= X12 ) )
| ~ ( in @ X10 @ X2 )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( in @ ( kpair @ X10 @ X12 ) @ X6 )
| ( ( ap @ X2 @ X4 @ X6 @ X10 )
= X12 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ~ ( in @ X10 @ X2 )
| ~ ( in @ X12 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl79,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i,X10: $i,X12: $i] :
( ~ ( in @ ( kpair @ X10 @ X12 ) @ X6 )
| ( ( ap @ X2 @ X4 @ X6 @ X10 )
= X12 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) )
!= ( setadjoin @ X8 @ emptyset ) )
| ~ ( in @ X8
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) )
| ~ ( in @ X10 @ X2 )
| ~ ( in @ X12 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( '#sk4' @ X0 @ '#sk2' @ '#sk5' ) @ '#sk1' )
| ~ ( in @ X1 @ '#sk2' )
| ~ ( in @ X2 @ X0 )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ ( '#sk4' @ X0 @ '#sk2' @ '#sk5' ) @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ ( '#sk8' @ ( '#sk4' @ X0 @ '#sk2' @ '#sk5' ) ) @ emptyset ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ X0 @ '#sk2' ) )
| ( ( ap @ X0 @ '#sk2' @ '#sk5' @ X2 )
= X1 )
| ~ ( in @ ( kpair @ X2 @ X1 ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl67,zip_derived_cl79]) ).
thf(zip_derived_cl68,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk8' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl73,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk8' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl633,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( kpair @ X2 @ X1 ) @ '#sk5' )
| ( ( ap @ X0 @ '#sk2' @ '#sk5' @ X2 )
= X1 )
| ~ ( subset @ '#sk5' @ ( cartprod @ X0 @ '#sk2' ) )
| ~ ( in @ X2 @ X0 )
| ~ ( in @ X1 @ '#sk2' )
| ~ ( in @ ( '#sk4' @ X0 @ '#sk2' @ '#sk5' ) @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl132,zip_derived_cl73]) ).
thf(zip_derived_cl635,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk2' )
| ~ ( in @ X1 @ '#sk1' )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X1 )
= X0 )
| ~ ( in @ ( kpair @ X1 @ X0 ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl578,zip_derived_cl633]) ).
thf(zip_derived_cl36_008,plain,
subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl637,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk2' )
| ~ ( in @ X1 @ '#sk1' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X1 )
= X0 )
| ~ ( in @ ( kpair @ X1 @ X0 ) @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl635,zip_derived_cl36]) ).
thf(zip_derived_cl639,plain,
! [X0: $i] :
( ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' )
| ( ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ '#sk7' )
= X0 )
| ~ ( in @ X0 @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl55,zip_derived_cl637]) ).
thf(zip_derived_cl463_009,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ ( kpair @ X0 @ ( ap @ '#sk1' @ '#sk2' @ '#sk5' @ X0 ) ) @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl449]) ).
thf(zip_derived_cl646,plain,
! [X0: $i] :
( ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk2' )
| ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' )
| ~ ( in @ '#sk7' @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl639,zip_derived_cl463]) ).
thf(zip_derived_cl55_010,plain,
in @ '#sk7' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl705,plain,
! [X0: $i] :
( ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk3' )
| ~ ( in @ X0 @ '#sk2' )
| ~ ( in @ ( kpair @ '#sk7' @ X0 ) @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl646,zip_derived_cl55]) ).
thf(zip_derived_cl722,plain,
( ~ ( in @ '#sk9' @ '#sk2' )
| ( in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl705]) ).
thf(zip_derived_cl69_011,plain,
in @ '#sk9' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl730,plain,
in @ ( kpair @ '#sk7' @ '#sk9' ) @ '#sk3',
inference(demod,[status(thm)],[zip_derived_cl722,zip_derived_cl69]) ).
thf(zip_derived_cl736,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl75,zip_derived_cl730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.26 % Problem : SEU687^2 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.27 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.aq1rYNDiXn true
% 0.12/0.49 % Computer : n008.cluster.edu
% 0.12/0.49 % Model : x86_64 x86_64
% 0.12/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.49 % Memory : 8042.1875MB
% 0.12/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.49 % CPULimit : 300
% 0.12/0.49 % WCLimit : 300
% 0.12/0.49 % DateTime : Wed Oct 1 16:15:38 EDT 2025
% 0.12/0.50 % CPUTime :
% 0.12/0.50 % Running portfolio for 300 s
% 0.12/0.50 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.52 % Number of cores: 8
% 0.12/0.53 % Python version: Python 3.6.8
% 0.12/0.54 % Running in HO mode
% 0.34/0.92 % Total configuration time : 828
% 0.34/0.92 % Estimated wc time : 1656
% 0.34/0.92 % Estimated cpu time (8 cpus) : 207.0
% 0.34/1.05 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.34/1.09 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.34/1.09 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.34/1.13 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.34/1.14 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.34/1.14 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.62/1.20 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.62/1.23 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 3.43/1.67 % Solved by lams/20_acsne_simpl.sh.
% 3.43/1.67 % done 149 iterations in 0.344s
% 3.43/1.67 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 3.43/1.67 % SZS output start Refutation
% See solution above
% 3.43/1.68
% 3.43/1.68
% 3.43/1.68 % Terminating...
% 3.80/1.85 % Runner terminated.
% 3.82/1.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------