TSTP Solution File: SEU823^2 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU823^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2hSuulKPPN true
% Computer : n015.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 19:18:30 EDT 2023
% Result : Theorem 6.68s 1.48s
% Output : Refutation 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 46
% Syntax : Number of formulae : 292 ( 81 unt; 23 typ; 0 def)
% Number of atoms : 2009 ( 130 equ; 41 cnn)
% Maximal formula atoms : 106 ( 7 avg)
% Number of connectives : 5765 ( 515 ~; 700 |; 165 &;3577 @)
% ( 0 <=>; 500 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 23 usr; 8 con; 0-2 aty)
% ( 281 !!; 27 ??; 0 @@+; 0 @@-)
% Number of variables : 666 ( 317 ^; 340 !; 9 ?; 666 :)
% Comments :
%------------------------------------------------------------------------------
thf(ordinalIrrefl_type,type,
ordinalIrrefl: $o ).
thf(stricttotalorderedByIn_type,type,
stricttotalorderedByIn: $i > $o ).
thf('#sk14_type',type,
'#sk14': $i > $i > $i ).
thf('#sk7_type',type,
'#sk7': $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf('#sk12_type',type,
'#sk12': $i > $i ).
thf('#form5_type',type,
'#form5': $i > $o ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf(ordinalTransSet_type,type,
ordinalTransSet: $o ).
thf('#sk4_type',type,
'#sk4': $i > $i ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf('#form11_type',type,
'#form11': $i > $o ).
thf('#sk3_type',type,
'#sk3': $i > $i ).
thf('#sk13_type',type,
'#sk13': $i > $i ).
thf(transitiveset_type,type,
transitiveset: $i > $o ).
thf('#sk10_type',type,
'#sk10': $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf('#sk6_type',type,
'#sk6': $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#form8_type',type,
'#form8': $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(wellorderedByIn_type,type,
wellorderedByIn: $i > $o ).
thf(ordinalIrrefl,axiom,
( ordinalIrrefl
= ( ! [X: $i] :
( ( ordinal @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ~ ( in @ A @ A ) ) ) ) ) ).
thf('0',plain,
( ordinalIrrefl
= ( ! [X4: $i] :
( ( ordinal @ X4 )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ~ ( in @ X6 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(ordinalTransSet,axiom,
( ordinalTransSet
= ( ! [X: $i] :
( ( ordinal @ X )
=> ! [Xx: $i,A: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) ) ) ).
thf('1',plain,
( ordinalTransSet
= ( ! [X4: $i] :
( ( ordinal @ X4 )
=> ! [X6: $i,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( in @ X6 @ X8 )
=> ( in @ X6 @ X4 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ordinal,axiom,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ) ).
thf(wellorderedByIn,axiom,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ) ).
thf(stricttotalorderedByIn,axiom,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ) ).
thf('2',plain,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( ( in @ Xx @ X )
& ( in @ X @ Y ) )
=> ( in @ Xx @ Y ) ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ! [Y: $i] :
( ( in @ Y @ A )
=> ( ( X = Y )
| ( in @ X @ Y )
| ( in @ Y @ X ) ) ) )
& ! [X: $i] :
( ( in @ X @ A )
=> ~ ( in @ X @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[stricttotalorderedByIn]) ).
thf('3',plain,
( stricttotalorderedByIn
= ( ^ [V_1: $i] :
( ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ! [X6: $i] :
( ( in @ X6 @ V_1 )
=> ! [X8: $i] :
( ( in @ X8 @ V_1 )
=> ( ( ( in @ X4 @ X6 )
& ( in @ X6 @ X8 ) )
=> ( in @ X4 @ X8 ) ) ) ) )
& ! [X10: $i] :
( ( in @ X10 @ V_1 )
=> ! [X12: $i] :
( ( in @ X12 @ V_1 )
=> ( ( X10 = X12 )
| ( in @ X10 @ X12 )
| ( in @ X12 @ X10 ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ V_1 )
=> ~ ( in @ X14 @ X14 ) ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( ( nonempty @ X )
=> ? [Xx: $i] :
( ! [Y: $i] :
( ( in @ Y @ X )
=> ( ( Xx = Y )
| ( in @ Xx @ Y ) ) )
& ( in @ Xx @ X ) ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[wellorderedByIn,'3']) ).
thf('5',plain,
( wellorderedByIn
= ( ^ [V_1: $i] :
( ( stricttotalorderedByIn @ V_1 )
& ! [X4: $i] :
( ( in @ X4 @ ( powerset @ V_1 ) )
=> ( ( nonempty @ X4 )
=> ? [X6: $i] :
( ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 = X8 )
| ( in @ X6 @ X8 ) ) )
& ( in @ X6 @ X4 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( ordinal
= ( ^ [Xx: $i] :
( ( transitiveset @ Xx )
& ( wellorderedByIn @ Xx ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ordinal,'5','3']) ).
thf('7',plain,
( ordinal
= ( ^ [V_1: $i] :
( ( transitiveset @ V_1 )
& ( wellorderedByIn @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(ordinalNoCycle,conjecture,
( ordinalTransSet
=> ( ordinalIrrefl
=> ! [X: $i] :
( ( ordinal @ X )
=> ! [A: $i] :
( ( in @ X @ A )
=> ~ ( in @ A @ X ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i] :
( ( ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X4 ) )
=> ( ( nonempty @ X18 )
=> ? [X20: $i] :
( ( in @ X20 @ X18 )
& ! [X22: $i] :
( ( in @ X22 @ X18 )
=> ( ( in @ X20 @ X22 )
| ( X20 = X22 ) ) ) ) ) )
& ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ~ ( in @ X16 @ X16 ) )
& ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ X14 @ X12 )
| ( in @ X12 @ X14 )
| ( X12 = X14 ) ) ) )
& ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( ( in @ X8 @ X10 )
& ( in @ X6 @ X8 ) )
=> ( in @ X6 @ X10 ) ) ) ) )
& ( transitiveset @ X4 ) )
=> ! [X24: $i,X26: $i] :
( ( in @ X26 @ X4 )
=> ( ( in @ X24 @ X26 )
=> ( in @ X24 @ X4 ) ) ) )
=> ( ! [X28: $i] :
( ( ! [X42: $i] :
( ( in @ X42 @ ( powerset @ X28 ) )
=> ( ( nonempty @ X42 )
=> ? [X44: $i] :
( ( in @ X44 @ X42 )
& ! [X46: $i] :
( ( in @ X46 @ X42 )
=> ( ( in @ X44 @ X46 )
| ( X44 = X46 ) ) ) ) ) )
& ! [X40: $i] :
( ( in @ X40 @ X28 )
=> ~ ( in @ X40 @ X40 ) )
& ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( ( in @ X38 @ X36 )
| ( in @ X36 @ X38 )
| ( X36 = X38 ) ) ) )
& ! [X30: $i] :
( ( in @ X30 @ X28 )
=> ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ( ( ( in @ X32 @ X34 )
& ( in @ X30 @ X32 ) )
=> ( in @ X30 @ X34 ) ) ) ) )
& ( transitiveset @ X28 ) )
=> ! [X48: $i] :
( ( in @ X48 @ X28 )
=> ~ ( in @ X48 @ X48 ) ) )
=> ! [X50: $i] :
( ( ! [X64: $i] :
( ( in @ X64 @ ( powerset @ X50 ) )
=> ( ( nonempty @ X64 )
=> ? [X66: $i] :
( ( in @ X66 @ X64 )
& ! [X68: $i] :
( ( in @ X68 @ X64 )
=> ( ( in @ X66 @ X68 )
| ( X66 = X68 ) ) ) ) ) )
& ! [X62: $i] :
( ( in @ X62 @ X50 )
=> ~ ( in @ X62 @ X62 ) )
& ! [X58: $i] :
( ( in @ X58 @ X50 )
=> ! [X60: $i] :
( ( in @ X60 @ X50 )
=> ( ( in @ X60 @ X58 )
| ( in @ X58 @ X60 )
| ( X58 = X60 ) ) ) )
& ! [X52: $i] :
( ( in @ X52 @ X50 )
=> ! [X54: $i] :
( ( in @ X54 @ X50 )
=> ! [X56: $i] :
( ( in @ X56 @ X50 )
=> ( ( ( in @ X54 @ X56 )
& ( in @ X52 @ X54 ) )
=> ( in @ X52 @ X56 ) ) ) ) )
& ( transitiveset @ X50 ) )
=> ! [X70: $i] :
( ( in @ X50 @ X70 )
=> ~ ( in @ X70 @ X50 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i] :
( ( ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X4 ) )
=> ( ( nonempty @ X18 )
=> ? [X20: $i] :
( ( in @ X20 @ X18 )
& ! [X22: $i] :
( ( in @ X22 @ X18 )
=> ( ( in @ X20 @ X22 )
| ( X20 = X22 ) ) ) ) ) )
& ! [X16: $i] :
( ( in @ X16 @ X4 )
=> ~ ( in @ X16 @ X16 ) )
& ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X4 )
=> ( ( in @ X14 @ X12 )
| ( in @ X12 @ X14 )
| ( X12 = X14 ) ) ) )
& ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( ( in @ X8 @ X10 )
& ( in @ X6 @ X8 ) )
=> ( in @ X6 @ X10 ) ) ) ) )
& ( transitiveset @ X4 ) )
=> ! [X24: $i,X26: $i] :
( ( in @ X26 @ X4 )
=> ( ( in @ X24 @ X26 )
=> ( in @ X24 @ X4 ) ) ) )
=> ( ! [X28: $i] :
( ( ! [X42: $i] :
( ( in @ X42 @ ( powerset @ X28 ) )
=> ( ( nonempty @ X42 )
=> ? [X44: $i] :
( ( in @ X44 @ X42 )
& ! [X46: $i] :
( ( in @ X46 @ X42 )
=> ( ( in @ X44 @ X46 )
| ( X44 = X46 ) ) ) ) ) )
& ! [X40: $i] :
( ( in @ X40 @ X28 )
=> ~ ( in @ X40 @ X40 ) )
& ! [X36: $i] :
( ( in @ X36 @ X28 )
=> ! [X38: $i] :
( ( in @ X38 @ X28 )
=> ( ( in @ X38 @ X36 )
| ( in @ X36 @ X38 )
| ( X36 = X38 ) ) ) )
& ! [X30: $i] :
( ( in @ X30 @ X28 )
=> ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ! [X34: $i] :
( ( in @ X34 @ X28 )
=> ( ( ( in @ X32 @ X34 )
& ( in @ X30 @ X32 ) )
=> ( in @ X30 @ X34 ) ) ) ) )
& ( transitiveset @ X28 ) )
=> ! [X48: $i] :
( ( in @ X48 @ X28 )
=> ~ ( in @ X48 @ X48 ) ) )
=> ! [X50: $i] :
( ( ! [X64: $i] :
( ( in @ X64 @ ( powerset @ X50 ) )
=> ( ( nonempty @ X64 )
=> ? [X66: $i] :
( ( in @ X66 @ X64 )
& ! [X68: $i] :
( ( in @ X68 @ X64 )
=> ( ( in @ X66 @ X68 )
| ( X66 = X68 ) ) ) ) ) )
& ! [X62: $i] :
( ( in @ X62 @ X50 )
=> ~ ( in @ X62 @ X62 ) )
& ! [X58: $i] :
( ( in @ X58 @ X50 )
=> ! [X60: $i] :
( ( in @ X60 @ X50 )
=> ( ( in @ X60 @ X58 )
| ( in @ X58 @ X60 )
| ( X58 = X60 ) ) ) )
& ! [X52: $i] :
( ( in @ X52 @ X50 )
=> ! [X54: $i] :
( ( in @ X54 @ X50 )
=> ! [X56: $i] :
( ( in @ X56 @ X50 )
=> ( ( ( in @ X54 @ X56 )
& ( in @ X52 @ X54 ) )
=> ( in @ X52 @ X56 ) ) ) ) )
& ( transitiveset @ X50 ) )
=> ! [X70: $i] :
( ( in @ X50 @ X70 )
=> ~ ( in @ X70 @ X50 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( (~) @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( (~) @ ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( (~) @ ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ '#sk1' ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( transitiveset @ '#sk1' ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ '#sk1' @ Y0 )
=> ( (~) @ ( in @ Y0 @ '#sk1' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ '#sk1' ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( transitiveset @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( (~) @ ( in @ X2 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X2 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl113,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl8,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ '#sk1' @ Y0 )
=> ( (~) @ ( in @ Y0 @ '#sk1' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
~ ( ( in @ '#sk1' @ '#sk2' )
=> ( (~) @ ( in @ '#sk2' @ '#sk1' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl21,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21_001,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22_002,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22_003,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21_004,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( ( nonempty @ Y1 )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
& ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
=> ( ( in @ Y2 @ Y3 )
| ( Y2 = Y3 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( (~) @ ( in @ Y1 @ Y1 ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y2 @ Y1 )
| ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( ( in @ Y2 @ Y3 )
& ( in @ Y1 @ Y2 ) )
=> ( in @ Y1 @ Y3 ) ) ) ) ) ) ) )
& ( transitiveset @ Y0 ) )
=> ( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( transitiveset @ X2 ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
! [X2: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( transitiveset @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl16,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
=> ( ( nonempty @ ( '#sk3' @ X2 ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl24,plain,
! [X2: $i] :
( ~ ( ( nonempty @ ( '#sk3' @ X2 ) )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ( nonempty @ ( '#sk3' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
( ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl35,plain,
! [X2: $i] :
( ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl38,plain,
! [X2: $i] :
( ~ ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ( nonempty @ ( '#sk3' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl35]) ).
thf(zip_derived_cl29_005,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl35_006,plain,
! [X2: $i] :
( ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl35]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( '#form5' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl38,zip_derived_cl43]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X4 @ Y0 )
=> ( in @ X4 @ X2 ) ) ) )
| ~ ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( transitiveset @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl35_007,plain,
! [X2: $i] :
( ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl39,plain,
! [X2: $i] :
( ~ ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl31,zip_derived_cl35]) ).
thf(zip_derived_cl43_008,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( '#form5' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl43]) ).
thf(zip_derived_cl60,plain,
! [X2: $i] :
( ( '#form11' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form11' @ X2 )
| ~ ( '#form8' @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X4 @ Y0 )
=> ( in @ X4 @ X2 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl59,zip_derived_cl60]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) ) )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ~ ( '#form8' @ X2 )
| ~ ( '#form11' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl93,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) )
| ~ ( '#form11' @ X2 )
| ~ ( '#form8' @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl101,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ( nonempty @ ( '#sk3' @ X2 ) )
| ~ ( '#form8' @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl507,plain,
! [X0: $i] :
( ~ ( in @ '#sk2' @ X0 )
| ~ ( '#form11' @ X0 )
| ~ ( '#form8' @ X0 )
| ( nonempty @ ( '#sk3' @ X0 ) )
| ~ ( transitiveset @ X0 )
| ~ ( '#form5' @ X0 )
| ( in @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl101]) ).
thf(zip_derived_cl529,plain,
( ( in @ '#sk1' @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ( nonempty @ ( '#sk3' @ '#sk1' ) )
| ~ ( '#form8' @ '#sk1' )
| ~ ( '#form11' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl507]) ).
thf(zip_derived_cl113_009,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl14,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl43_010,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk9' @ X2 ) @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( '#sk9' @ X2 ) )
| ( in @ ( '#sk9' @ X2 ) @ Y0 )
| ( ( '#sk9' @ X2 )
= Y0 ) ) ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl56,plain,
! [X2: $i] :
( ( in @ ( '#sk9' @ X2 ) @ X2 )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl57,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ Y0 @ ( '#sk9' @ X2 ) )
| ( in @ ( '#sk9' @ X2 ) @ Y0 )
| ( ( '#sk9' @ X2 )
= Y0 ) ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl68,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk12' @ X2 ) @ X2 )
=> ( ( in @ ( '#sk12' @ X2 ) @ ( '#sk9' @ X2 ) )
| ( in @ ( '#sk9' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( ( '#sk9' @ X2 )
= ( '#sk12' @ X2 ) ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl79,plain,
! [X2: $i] :
( ( in @ ( '#sk12' @ X2 ) @ X2 )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( in @ Y0 @ X2 )
| ( in @ X2 @ Y0 )
| ( X2 = Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( in @ Y0 @ X2 )
| ( in @ X2 @ Y0 )
| ( X2 = Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ '#sk1' )
=> ( ( in @ X4 @ X2 )
| ( in @ X2 @ X4 )
| ( X2 = X4 ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ '#sk1' )
| ( in @ X4 @ X2 )
| ( in @ X2 @ X4 )
| ( X2 = X4 )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ X2 )
| ( in @ X2 @ X4 )
| ( X2 = X4 )
| ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ X2 )
| ( in @ X2 @ X4 )
| ( X2 = X4 )
| ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl132,plain,
! [X0: $i] :
( ( '#form8' @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( ( '#sk12' @ '#sk1' )
= X0 )
| ( in @ ( '#sk12' @ '#sk1' ) @ X0 )
| ( in @ X0 @ ( '#sk12' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl64]) ).
thf(zip_derived_cl310,plain,
( ( '#form8' @ '#sk1' )
| ( in @ ( '#sk9' @ '#sk1' ) @ ( '#sk12' @ '#sk1' ) )
| ( in @ ( '#sk12' @ '#sk1' ) @ ( '#sk9' @ '#sk1' ) )
| ( ( '#sk12' @ '#sk1' )
= ( '#sk9' @ '#sk1' ) )
| ( '#form8' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl132]) ).
thf(zip_derived_cl322,plain,
( ( ( '#sk12' @ '#sk1' )
= ( '#sk9' @ '#sk1' ) )
| ( in @ ( '#sk12' @ '#sk1' ) @ ( '#sk9' @ '#sk1' ) )
| ( in @ ( '#sk9' @ '#sk1' ) @ ( '#sk12' @ '#sk1' ) )
| ( '#form8' @ '#sk1' ) ),
inference(simplify,[status(thm)],[zip_derived_cl310]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk12' @ X2 ) @ ( '#sk9' @ X2 ) )
| ( in @ ( '#sk9' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( ( '#sk9' @ X2 )
= ( '#sk12' @ X2 ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl90,plain,
! [X2: $i] :
( ( ( '#sk9' @ X2 )
!= ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl98,plain,
! [X2: $i] :
( ( ( '#sk9' @ X2 )
!= ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl419,plain,
( ( '#form8' @ '#sk1' )
| ( in @ ( '#sk9' @ '#sk1' ) @ ( '#sk12' @ '#sk1' ) )
| ( in @ ( '#sk12' @ '#sk1' ) @ ( '#sk9' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl322,zip_derived_cl98]) ).
thf(zip_derived_cl89,plain,
! [X2: $i] :
( ~ ( in @ ( '#sk9' @ X2 ) @ ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl420,plain,
( ( in @ ( '#sk12' @ '#sk1' ) @ ( '#sk9' @ '#sk1' ) )
| ( '#form8' @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl419,zip_derived_cl89]) ).
thf(zip_derived_cl88,plain,
! [X2: $i] :
( ~ ( in @ ( '#sk12' @ X2 ) @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl421,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl60_011,plain,
! [X2: $i] :
( ( '#form11' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) )
| ( '#form11' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl73,plain,
! [X2: $i] :
( ( in @ ( '#sk4' @ X2 ) @ X2 )
| ( '#form11' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl26_012,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X2 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl123,plain,
( ( '#form11' @ '#sk1' )
| ~ ( in @ ( '#sk4' @ '#sk1' ) @ ( '#sk4' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl26]) ).
thf(zip_derived_cl74,plain,
! [X2: $i] :
( ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) )
| ( '#form11' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl129,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl531,plain,
( ~ ( '#form5' @ '#sk1' )
| ( nonempty @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl529,zip_derived_cl113,zip_derived_cl14,zip_derived_cl421,zip_derived_cl129]) ).
thf(zip_derived_cl10,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ '#sk1' ) )
=> ( ( nonempty @ Y0 )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ( in @ X2 @ ( powerset @ '#sk1' ) )
=> ( ( nonempty @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ( ( nonempty @ X2 )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ~ ( nonempty @ X2 )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl40,plain,
! [X2: $i] :
( ( ( in @ ( '#sk7' @ X2 ) @ X2 )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( '#sk7' @ X2 ) @ Y0 )
| ( ( '#sk7' @ X2 )
= Y0 ) ) ) ) )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ~ ( nonempty @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl50,plain,
! [X2: $i] :
( ( in @ ( '#sk7' @ X2 ) @ X2 )
| ~ ( nonempty @ X2 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl533,plain,
( ~ ( '#form5' @ '#sk1' )
| ~ ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl531,zip_derived_cl50]) ).
thf(zip_derived_cl35_013,plain,
! [X2: $i] :
( ( '#form5' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl36,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk6' @ X2 ) @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ ( '#sk6' @ X2 ) @ Y0 ) )
=> ( in @ ( '#sk6' @ X2 ) @ Y1 ) ) ) ) ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ ( '#sk6' @ X2 ) @ Y0 ) )
=> ( in @ ( '#sk6' @ X2 ) @ Y1 ) ) ) ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl58,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk10' @ X2 ) @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ( in @ ( '#sk10' @ X2 ) @ Y0 )
& ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) )
=> ( in @ ( '#sk6' @ X2 ) @ Y0 ) ) ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl70,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( ( in @ ( '#sk10' @ X2 ) @ Y0 )
& ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) )
=> ( in @ ( '#sk6' @ X2 ) @ Y0 ) ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ~ ( ( in @ ( '#sk13' @ X2 ) @ X2 )
=> ( ( ( in @ ( '#sk10' @ X2 ) @ ( '#sk13' @ X2 ) )
& ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) )
=> ( in @ ( '#sk6' @ X2 ) @ ( '#sk13' @ X2 ) ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl92,plain,
! [X2: $i] :
( ~ ( ( ( in @ ( '#sk10' @ X2 ) @ ( '#sk13' @ X2 ) )
& ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) )
=> ( in @ ( '#sk6' @ X2 ) @ ( '#sk13' @ X2 ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl99,plain,
! [X2: $i] :
( ( ( in @ ( '#sk10' @ X2 ) @ ( '#sk13' @ X2 ) )
& ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl104,plain,
! [X2: $i] :
( ( in @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl69,plain,
! [X2: $i] :
( ( in @ ( '#sk10' @ X2 ) @ X2 )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl103,plain,
! [X2: $i] :
( ( in @ ( '#sk10' @ X2 ) @ ( '#sk13' @ X2 ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ X2 @ Y0 ) )
=> ( in @ X2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ X2 @ Y0 ) )
=> ( in @ X2 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( ( in @ X4 @ Y0 )
& ( in @ X2 @ X4 ) )
=> ( in @ X2 @ Y0 ) ) ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ '#sk1' )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( ( in @ X4 @ Y0 )
& ( in @ X2 @ X4 ) )
=> ( in @ X2 @ Y0 ) ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ '#sk1' )
=> ( ( ( in @ X4 @ X6 )
& ( in @ X2 @ X4 ) )
=> ( in @ X2 @ X6 ) ) )
| ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ '#sk1' )
| ( ( ( in @ X4 @ X6 )
& ( in @ X2 @ X4 ) )
=> ( in @ X2 @ X6 ) )
| ~ ( in @ X4 @ '#sk1' )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ X4 @ X6 )
& ( in @ X2 @ X4 ) )
| ( in @ X2 @ X6 )
| ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' )
| ~ ( in @ X6 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X4 @ X6 )
| ~ ( in @ X2 @ X4 )
| ~ ( in @ X6 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' )
| ~ ( in @ X2 @ '#sk1' )
| ( in @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl177,plain,
! [X0: $i,X1: $i] :
( ( '#form5' @ X0 )
| ( in @ X1 @ ( '#sk13' @ X0 ) )
| ~ ( in @ X1 @ '#sk1' )
| ~ ( in @ ( '#sk10' @ X0 ) @ '#sk1' )
| ~ ( in @ ( '#sk13' @ X0 ) @ '#sk1' )
| ~ ( in @ X1 @ ( '#sk10' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl103,zip_derived_cl85]) ).
thf(zip_derived_cl556,plain,
! [X0: $i] :
( ( '#form5' @ '#sk1' )
| ~ ( in @ X0 @ ( '#sk10' @ '#sk1' ) )
| ~ ( in @ ( '#sk13' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ X0 @ ( '#sk13' @ '#sk1' ) )
| ( '#form5' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl177]) ).
thf(zip_derived_cl558,plain,
! [X0: $i] :
( ( in @ X0 @ ( '#sk13' @ '#sk1' ) )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( in @ ( '#sk13' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ ( '#sk10' @ '#sk1' ) )
| ( '#form5' @ '#sk1' ) ),
inference(simplify,[status(thm)],[zip_derived_cl556]) ).
thf(zip_derived_cl91,plain,
! [X2: $i] :
( ( in @ ( '#sk13' @ X2 ) @ X2 )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl560,plain,
! [X0: $i] :
( ( '#form5' @ '#sk1' )
| ~ ( in @ X0 @ ( '#sk10' @ '#sk1' ) )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ X0 @ ( '#sk13' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl558,zip_derived_cl91]) ).
thf(zip_derived_cl565,plain,
( ( '#form5' @ '#sk1' )
| ( in @ ( '#sk6' @ '#sk1' ) @ ( '#sk13' @ '#sk1' ) )
| ~ ( in @ ( '#sk6' @ '#sk1' ) @ '#sk1' )
| ( '#form5' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl560]) ).
thf(zip_derived_cl575,plain,
( ~ ( in @ ( '#sk6' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk6' @ '#sk1' ) @ ( '#sk13' @ '#sk1' ) )
| ( '#form5' @ '#sk1' ) ),
inference(simplify,[status(thm)],[zip_derived_cl565]) ).
thf(zip_derived_cl46,plain,
! [X2: $i] :
( ( in @ ( '#sk6' @ X2 ) @ X2 )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl577,plain,
( ( '#form5' @ '#sk1' )
| ( in @ ( '#sk6' @ '#sk1' ) @ ( '#sk13' @ '#sk1' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl575,zip_derived_cl46]) ).
thf(zip_derived_cl100,plain,
! [X2: $i] :
( ~ ( in @ ( '#sk6' @ X2 ) @ ( '#sk13' @ X2 ) )
| ( '#form5' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl578,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl580,plain,
( ~ ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl578]) ).
thf(zip_derived_cl22_014,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21_015,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl37_016,plain,
! [X2: $i] :
( ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl29,zip_derived_cl35]) ).
thf(zip_derived_cl43_017,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( ( in @ ( '#sk4' @ X2 ) @ X2 )
=> ( (~) @ ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( '#form5' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl37,zip_derived_cl43]) ).
thf(zip_derived_cl55,plain,
! [X2: $i] :
( ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X4 @ Y0 )
=> ( in @ X4 @ X2 ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) ) )
| ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ ( '#sk4' @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl464,plain,
! [X0: $i] :
( ~ ( in @ '#sk2' @ X0 )
| ~ ( '#form8' @ X0 )
| ~ ( transitiveset @ X0 )
| ( in @ ( '#sk3' @ X0 ) @ ( powerset @ X0 ) )
| ~ ( '#form5' @ X0 )
| ( in @ ( '#sk4' @ X0 ) @ ( '#sk4' @ X0 ) )
| ( in @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl97]) ).
thf(zip_derived_cl1718,plain,
( ( in @ '#sk1' @ '#sk1' )
| ( in @ ( '#sk4' @ '#sk1' ) @ ( '#sk4' @ '#sk1' ) )
| ~ ( '#form5' @ '#sk1' )
| ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl464]) ).
thf(zip_derived_cl113_018,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl21_019,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21_020,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22_021,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22_022,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21_023,plain,
in @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ( in @ ( '#sk4' @ X2 ) @ X2 )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X4 @ Y0 )
=> ( in @ X4 @ X2 ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) ) )
| ( in @ ( '#sk4' @ X2 ) @ X2 )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ( in @ ( '#sk4' @ X2 ) @ X2 )
| ~ ( '#form5' @ X2 )
| ( in @ ( '#sk3' @ X2 ) @ ( powerset @ X2 ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl364,plain,
! [X0: $i] :
( ~ ( in @ '#sk2' @ X0 )
| ~ ( '#form8' @ X0 )
| ~ ( transitiveset @ X0 )
| ( in @ ( '#sk3' @ X0 ) @ ( powerset @ X0 ) )
| ~ ( '#form5' @ X0 )
| ( in @ ( '#sk4' @ X0 ) @ X0 )
| ( in @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl96]) ).
thf(zip_derived_cl767,plain,
( ( in @ '#sk1' @ '#sk1' )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl364]) ).
thf(zip_derived_cl113_024,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl578_025,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_026,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_027,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl769,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl767,zip_derived_cl113,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl580_028,plain,
( ~ ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl578]) ).
thf(zip_derived_cl771,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl769,zip_derived_cl580]) ).
thf(zip_derived_cl49_029,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( '#form5' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl39,zip_derived_cl43]) ).
thf(zip_derived_cl60_030,plain,
! [X2: $i] :
( ( '#form11' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ X2 ) ) ) ) )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( '#form8' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl49,zip_derived_cl60]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ X4 @ Y0 )
=> ( in @ X4 @ X2 ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) ) )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl94,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( ( in @ X4 @ X6 )
=> ( in @ X4 @ X2 ) )
| ~ ( '#form8' @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl102,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( '#sk3' @ X2 ) )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl105,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8 @ ( '#sk3' @ X2 ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
=> ( ( in @ X8 @ Y0 )
| ( X8 = Y0 ) ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl106,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( '#sk3' @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( '#sk3' @ X2 ) )
=> ( ( in @ X8 @ Y0 )
| ( X8 = Y0 ) ) ) )
| ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl107,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ ( '#sk14' @ X2 @ X8 ) @ ( '#sk3' @ X2 ) )
=> ( ( in @ X8 @ ( '#sk14' @ X2 @ X8 ) )
| ( X8
= ( '#sk14' @ X2 @ X8 ) ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl108,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( '#sk14' @ X2 @ X8 ) @ ( '#sk3' @ X2 ) )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) )
| ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl812,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl771,zip_derived_cl108]) ).
thf(zip_derived_cl421_031,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl14_032,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl578_033,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl129_034,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl837,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl812,zip_derived_cl421,zip_derived_cl14,zip_derived_cl578,zip_derived_cl129]) ).
thf(zip_derived_cl1063,plain,
! [X0: $i] :
( ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) )
| ~ ( in @ X0 @ '#sk2' )
| ( in @ X0 @ '#sk1' )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl837]) ).
thf(zip_derived_cl1091,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ '#sk1' @ '#sk1' )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl1063]) ).
thf(zip_derived_cl113_035,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl1099,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1091,zip_derived_cl113]) ).
thf(zip_derived_cl769_036,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl767,zip_derived_cl113,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( '#sk7' @ X2 ) @ Y0 )
| ( ( '#sk7' @ X2 )
= Y0 ) ) ) )
| ~ ( nonempty @ X2 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ X2 )
=> ( ( in @ ( '#sk7' @ X2 ) @ X4 )
| ( ( '#sk7' @ X2 )
= X4 ) ) )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ~ ( nonempty @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ X2 )
| ( in @ ( '#sk7' @ X2 ) @ X4 )
| ( ( '#sk7' @ X2 )
= X4 )
| ~ ( nonempty @ X2 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk7' @ X2 ) @ X4 )
| ( ( '#sk7' @ X2 )
= X4 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ~ ( nonempty @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl95,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk7' @ X2 ) @ X4 )
| ( ( '#sk7' @ X2 )
= X4 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ~ ( nonempty @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl772,plain,
! [X0: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ ( '#sk3' @ '#sk1' ) )
| ~ ( nonempty @ ( '#sk3' @ '#sk1' ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= X0 )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl769,zip_derived_cl95]) ).
thf(zip_derived_cl531_037,plain,
( ~ ( '#form5' @ '#sk1' )
| ( nonempty @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl529,zip_derived_cl113,zip_derived_cl14,zip_derived_cl421,zip_derived_cl129]) ).
thf(zip_derived_cl578_038,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl579,plain,
nonempty @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl531,zip_derived_cl578]) ).
thf(zip_derived_cl796,plain,
! [X0: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X0 @ ( '#sk3' @ '#sk1' ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= X0 )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl772,zip_derived_cl579]) ).
thf(zip_derived_cl1105,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1099,zip_derived_cl796]) ).
thf(zip_derived_cl1134,plain,
( ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1105]) ).
thf(zip_derived_cl109,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ X8 @ ( '#sk14' @ X2 @ X8 ) )
| ( X8
= ( '#sk14' @ X2 @ X8 ) ) )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) )
| ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl110,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( '#sk14' @ X2 @ X8 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl1142,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ~ ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1134,zip_derived_cl110]) ).
thf(zip_derived_cl129_039,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl578_040,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_041,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_042,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl1165,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ~ ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl1142,zip_derived_cl129,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl771_043,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl769,zip_derived_cl580]) ).
thf(zip_derived_cl111,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( X8
!= ( '#sk14' @ X2 @ X8 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl112,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( X8
!= ( '#sk14' @ X2 @ X8 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl811,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
!= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl771,zip_derived_cl112]) ).
thf(zip_derived_cl129_044,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl578_045,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_046,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_047,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl836,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
!= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl811,zip_derived_cl129,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl1406,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ~ ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl1165,zip_derived_cl836]) ).
thf(zip_derived_cl771_048,plain,
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl769,zip_derived_cl580]) ).
thf(zip_derived_cl1407,plain,
! [X0: $i,X1: $i] :
( ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(clc,[status(thm)],[zip_derived_cl1406,zip_derived_cl771]) ).
thf(zip_derived_cl1430,plain,
( ~ ( in @ '#sk2' @ '#sk1' )
| ( in @ '#sk1' @ '#sk1' )
| ( in @ ( '#sk4' @ '#sk1' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl1407]) ).
thf(zip_derived_cl22_049,plain,
in @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl113_050,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl1473,plain,
in @ ( '#sk4' @ '#sk1' ) @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl1430,zip_derived_cl22,zip_derived_cl113]) ).
thf(zip_derived_cl26_051,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X2 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl1496,plain,
~ ( in @ ( '#sk4' @ '#sk1' ) @ ( '#sk4' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1473,zip_derived_cl26]) ).
thf(zip_derived_cl578_052,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_053,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_054,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl1720,plain,
in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl1718,zip_derived_cl113,zip_derived_cl1496,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl1722,plain,
in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl580,zip_derived_cl1720]) ).
thf(zip_derived_cl108_055,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( '#sk14' @ X2 @ X8 ) @ ( '#sk3' @ X2 ) )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) )
| ~ ( in @ X4 @ X6 )
| ( in @ X4 @ X2 )
| ~ ( '#form11' @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl1767,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1722,zip_derived_cl108]) ).
thf(zip_derived_cl421_056,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl14_057,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl578_058,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl129_059,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl1799,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1767,zip_derived_cl421,zip_derived_cl14,zip_derived_cl578,zip_derived_cl129]) ).
thf(zip_derived_cl2026,plain,
! [X0: $i] :
( ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) )
| ~ ( in @ X0 @ '#sk2' )
| ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl1799]) ).
thf(zip_derived_cl2059,plain,
( ( in @ '#sk1' @ '#sk1' )
| ( in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl2026]) ).
thf(zip_derived_cl113_060,plain,
~ ( in @ '#sk1' @ '#sk1' ),
inference(eq_fact,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl2069,plain,
in @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl2059,zip_derived_cl113]) ).
thf(zip_derived_cl1720_061,plain,
in @ ( '#sk3' @ '#sk1' ) @ ( powerset @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl1718,zip_derived_cl113,zip_derived_cl1496,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl95_062,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk7' @ X2 ) @ X4 )
| ( ( '#sk7' @ X2 )
= X4 )
| ~ ( in @ X2 @ ( powerset @ '#sk1' ) )
| ~ ( nonempty @ X2 )
| ~ ( in @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl1723,plain,
! [X0: $i] :
( ~ ( in @ X0 @ ( '#sk3' @ '#sk1' ) )
| ~ ( nonempty @ ( '#sk3' @ '#sk1' ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= X0 )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1720,zip_derived_cl95]) ).
thf(zip_derived_cl579_063,plain,
nonempty @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl531,zip_derived_cl578]) ).
thf(zip_derived_cl1750,plain,
! [X0: $i] :
( ~ ( in @ X0 @ ( '#sk3' @ '#sk1' ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= X0 )
| ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl1723,zip_derived_cl579]) ).
thf(zip_derived_cl2090,plain,
( ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2069,zip_derived_cl1750]) ).
thf(zip_derived_cl110_064,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( '#sk14' @ X2 @ X8 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl2187,plain,
! [X0: $i,X1: $i] :
( ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ~ ( in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ) )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2090,zip_derived_cl110]) ).
thf(zip_derived_cl1722_065,plain,
in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl580,zip_derived_cl1720]) ).
thf(zip_derived_cl129_066,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl578_067,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_068,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_069,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl2214,plain,
! [X0: $i,X1: $i] :
( ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) )
| ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl2187,zip_derived_cl1722,zip_derived_cl129,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl1722_070,plain,
in @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) @ ( '#sk3' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl580,zip_derived_cl1720]) ).
thf(zip_derived_cl112_071,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( X8
!= ( '#sk14' @ X2 @ X8 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( transitiveset @ X2 )
| ~ ( '#form5' @ X2 )
| ~ ( '#form11' @ X2 )
| ( in @ X4 @ X2 )
| ~ ( in @ X4 @ X6 )
| ~ ( in @ X8 @ ( '#sk3' @ X2 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl1766,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( '#form11' @ '#sk1' )
| ~ ( '#form5' @ '#sk1' )
| ~ ( transitiveset @ '#sk1' )
| ~ ( '#form8' @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
!= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1722,zip_derived_cl112]) ).
thf(zip_derived_cl129_072,plain,
'#form11' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl123,zip_derived_cl74]) ).
thf(zip_derived_cl578_073,plain,
'#form5' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl577,zip_derived_cl100]) ).
thf(zip_derived_cl14_074,plain,
transitiveset @ '#sk1',
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl421_075,plain,
'#form8' @ '#sk1',
inference(clc,[status(thm)],[zip_derived_cl420,zip_derived_cl88]) ).
thf(zip_derived_cl1798,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X0 @ '#sk1' )
| ( ( '#sk7' @ ( '#sk3' @ '#sk1' ) )
!= ( '#sk14' @ '#sk1' @ ( '#sk7' @ ( '#sk3' @ '#sk1' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1766,zip_derived_cl129,zip_derived_cl578,zip_derived_cl14,zip_derived_cl421]) ).
thf(zip_derived_cl2221,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ '#sk1' )
| ( in @ X1 @ '#sk1' )
| ~ ( in @ X1 @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl2214,zip_derived_cl1798]) ).
thf(zip_derived_cl2231,plain,
! [X0: $i] :
( ~ ( in @ X0 @ '#sk2' )
| ( in @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl22,zip_derived_cl2221]) ).
thf(zip_derived_cl2265,plain,
in @ '#sk1' @ '#sk1',
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl2231]) ).
thf(zip_derived_cl2306,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl113,zip_derived_cl2265]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU823^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.2hSuulKPPN true
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 18:11:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 6.68/1.48 % Solved by lams/20_acsne_simpl.sh.
% 6.68/1.48 % done 382 iterations in 0.602s
% 6.68/1.48 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 6.68/1.48 % SZS output start Refutation
% See solution above
% 6.68/1.48
% 6.68/1.48
% 6.68/1.48 % Terminating...
% 7.39/1.58 % Runner terminated.
% 7.39/1.60 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------