TSTP Solution File: SEU820^2 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU820^2 : 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.KNnaiN1CJS true
% Computer : n016.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 19:18:27 EDT 2023
% Result : Theorem 1.48s 0.84s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 47
% Syntax : Number of formulae : 117 ( 43 unt; 20 typ; 0 def)
% Number of atoms : 842 ( 93 equ; 18 cnn)
% Maximal formula atoms : 42 ( 8 avg)
% Number of connectives : 2041 ( 151 ~; 161 |; 76 &;1194 @)
% ( 0 <=>; 285 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 16 con; 0-2 aty)
% ( 167 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 283 ( 190 ^; 88 !; 5 ?; 283 :)
% Comments :
%------------------------------------------------------------------------------
thf(powersetE1_type,type,
powersetE1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf('#form8_type',type,
'#form8': $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subsetemptysetimpeq_type,type,
subsetemptysetimpeq: $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf('#form4_type',type,
'#form4': $o ).
thf('#form6_type',type,
'#form6': $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(vacuousDall_type,type,
vacuousDall: $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(nonempty_type,type,
nonempty: $i > $o ).
thf('#sk7_type',type,
'#sk7': $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk9_type',type,
'#sk9': $i ).
thf(wellorderedByIn_type,type,
wellorderedByIn: $i > $o ).
thf(stricttotalorderedByIn_type,type,
stricttotalorderedByIn: $i > $o ).
thf(transitiveset_type,type,
transitiveset: $i > $o ).
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('0',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('1',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(nonempty,axiom,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
thf('2',plain,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[nonempty]) ).
thf('3',plain,
( nonempty
= ( ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
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,'1','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','1','3']) ).
thf('7',plain,
( ordinal
= ( ^ [V_1: $i] :
( ( transitiveset @ V_1 )
& ( wellorderedByIn @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(transitiveset,axiom,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ) ).
thf('8',plain,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[transitiveset]) ).
thf('9',plain,
( transitiveset
= ( ^ [V_1: $i] :
! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( subset @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(powersetE1,axiom,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ) ).
thf('10',plain,
( powersetE1
= ( ! [X4: $i,X6: $i] :
( ( in @ X6 @ ( powerset @ X4 ) )
=> ( subset @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(subsetemptysetimpeq,axiom,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ) ).
thf('11',plain,
( subsetemptysetimpeq
= ( ! [X4: $i] :
( ( subset @ X4 @ emptyset )
=> ( X4 = emptyset ) ) ) ),
define([status(thm)]) ).
thf(vacuousDall,axiom,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ) ).
thf('12',plain,
( vacuousDall
= ( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(emptysetOrdinal,conjecture,
( vacuousDall
=> ( subsetemptysetimpeq
=> ( powersetE1
=> ( ordinal @ emptyset ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) )
=> ( ! [X8: $i] :
( ( subset @ X8 @ emptyset )
=> ( X8 = emptyset ) )
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( powerset @ X10 ) )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X28: $i] :
( ( in @ X28 @ ( powerset @ emptyset ) )
=> ( ( X28 != emptyset )
=> ? [X30: $i] :
( ( in @ X30 @ X28 )
& ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( in @ X30 @ X32 )
| ( X30 = X32 ) ) ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ emptyset )
=> ~ ( in @ X26 @ X26 ) )
& ! [X22: $i] :
( ( in @ X22 @ emptyset )
=> ! [X24: $i] :
( ( in @ X24 @ emptyset )
=> ( ( in @ X24 @ X22 )
| ( in @ X22 @ X24 )
| ( X22 = X24 ) ) ) )
& ! [X16: $i] :
( ( in @ X16 @ emptyset )
=> ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $i] :
( ( in @ X20 @ emptyset )
=> ( ( ( in @ X18 @ X20 )
& ( in @ X16 @ X18 ) )
=> ( in @ X16 @ X20 ) ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ emptyset )
=> ( subset @ X14 @ emptyset ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i > $o,X6: $i] :
( ( in @ X6 @ emptyset )
=> ( X4 @ X6 ) )
=> ( ! [X8: $i] :
( ( subset @ X8 @ emptyset )
=> ( X8 = emptyset ) )
=> ( ! [X10: $i,X12: $i] :
( ( in @ X12 @ ( powerset @ X10 ) )
=> ( subset @ X12 @ X10 ) )
=> ( ! [X28: $i] :
( ( in @ X28 @ ( powerset @ emptyset ) )
=> ( ( X28 != emptyset )
=> ? [X30: $i] :
( ( in @ X30 @ X28 )
& ! [X32: $i] :
( ( in @ X32 @ X28 )
=> ( ( in @ X30 @ X32 )
| ( X30 = X32 ) ) ) ) ) )
& ! [X26: $i] :
( ( in @ X26 @ emptyset )
=> ~ ( in @ X26 @ X26 ) )
& ! [X22: $i] :
( ( in @ X22 @ emptyset )
=> ! [X24: $i] :
( ( in @ X24 @ emptyset )
=> ( ( in @ X24 @ X22 )
| ( in @ X22 @ X24 )
| ( X22 = X24 ) ) ) )
& ! [X16: $i] :
( ( in @ X16 @ emptyset )
=> ! [X18: $i] :
( ( in @ X18 @ emptyset )
=> ! [X20: $i] :
( ( in @ X20 @ emptyset )
=> ( ( ( in @ X18 @ X20 )
& ( in @ X16 @ X18 ) )
=> ( in @ X16 @ X20 ) ) ) ) )
& ! [X14: $i] :
( ( in @ X14 @ emptyset )
=> ( subset @ X14 @ emptyset ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( Y0 @ Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
! [X2: $i > $o,X4: $i] :
( ( in @ X4 @ emptyset )
=> ( X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
! [X2: $o,X4: $i] :
( ( in @ X4 @ emptyset )
=> ( ^ [Y0: $i] : X2
@ X4 ) ),
inference(prune_arg_fun,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
! [X2: $o,X4: $i] :
( ( in @ X4 @ emptyset )
=> X2 ),
inference(ho_norm,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
! [X2: $o,X4: $i] :
( ~ ( in @ X4 @ emptyset )
| X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl93,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( Y0 = emptyset ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
& ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl15,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ emptyset ) )
=> ( ( Y0 != emptyset )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
& ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( in @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl18,plain,
( ~ ( ( in @ '#sk2' @ ( powerset @ emptyset ) )
=> ( ( '#sk2' != emptyset )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk2' )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
( ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl22,plain,
( ~ ( ( in @ '#sk3' @ emptyset )
=> ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ( in @ '#sk2' @ ( powerset @ emptyset ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl25,plain,
( ( in @ '#sk3' @ emptyset )
| ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl25_001,plain,
( ( in @ '#sk3' @ emptyset )
| ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl32,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl34,plain,
( ~ '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ( in @ '#sk3' @ emptyset ) ),
inference(renaming,[status(thm)],[zip_derived_cl25,zip_derived_cl32]) ).
thf(zip_derived_cl21,plain,
( ~ ( ( '#sk2' != emptyset )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk2' )
& ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk2' )
=> ( ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl23,plain,
( ( '#sk2' != emptyset )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
( ( '#sk2' != emptyset )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl40,plain,
( ~ '#form4'
| ( in @ '#sk3' @ emptyset )
| ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ '#form6' ),
inference(renaming,[status(thm)],[zip_derived_cl34,zip_derived_cl28]) ).
thf(zip_derived_cl27_002,plain,
( ( '#sk2' != emptyset )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28_003,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl30,plain,
( ~ '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ( '#sk2' != emptyset ) ),
inference(renaming,[status(thm)],[zip_derived_cl27,zip_derived_cl28]) ).
thf(zip_derived_cl32_004,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl36,plain,
( ~ '#form6'
| ( '#sk2' != emptyset )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ '#form4' ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).
thf(zip_derived_cl44,plain,
( '#form8'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl48,plain,
( ~ '#form8'
| ~ '#form6'
| ( in @ '#sk2' @ ( powerset @ emptyset ) )
| ( in @ '#sk3' @ emptyset )
| ~ '#form4' ),
inference(renaming,[status(thm)],[zip_derived_cl40,zip_derived_cl44]) ).
thf(zip_derived_cl44_005,plain,
( '#form8'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( in @ '#sk9' @ emptyset )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( ( in @ Y0 @ Y1 )
& ( in @ '#sk9' @ Y0 ) )
=> ( in @ '#sk9' @ Y1 ) ) ) ) ) ) )
| '#form8' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl52,plain,
( ( in @ '#sk9' @ emptyset )
| '#form8' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl93_006,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl100,plain,
'#form8',
inference(clc,[status(thm)],[zip_derived_cl52,zip_derived_cl93]) ).
thf(zip_derived_cl32_007,plain,
( '#form6'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( ( in @ Y1 @ Y0 )
| ( in @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl33,plain,
( ~ ( ( in @ '#sk7' @ emptyset )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( ( in @ Y0 @ '#sk7' )
| ( in @ '#sk7' @ Y0 )
| ( '#sk7' = Y0 ) ) ) ) )
| '#form6' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl41,plain,
( ( in @ '#sk7' @ emptyset )
| '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl93_008,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl99,plain,
'#form6',
inference(clc,[status(thm)],[zip_derived_cl41,zip_derived_cl93]) ).
thf(zip_derived_cl93_009,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl28_010,plain,
( '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( subset @ Y0 @ emptyset ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl29,plain,
( ~ ( ( in @ '#sk5' @ emptyset )
=> ( subset @ '#sk5' @ emptyset ) )
| '#form4' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl37,plain,
( ( in @ '#sk5' @ emptyset )
| '#form4' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl93_011,plain,
! [X0: $i] :
~ ( in @ X0 @ emptyset ),
inference('ho.refine',[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl98,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl37,zip_derived_cl93]) ).
thf(zip_derived_cl115,plain,
in @ '#sk2' @ ( powerset @ emptyset ),
inference(demod,[status(thm)],[zip_derived_cl48,zip_derived_cl100,zip_derived_cl99,zip_derived_cl93,zip_derived_cl98]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( subset @ Y1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( powerset @ X2 ) )
=> ( subset @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( subset @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( subset @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl116,plain,
subset @ '#sk2' @ emptyset,
inference('sup-',[status(thm)],[zip_derived_cl115,zip_derived_cl19]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ emptyset )
=> ( Y0 = emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
( ( subset @ X2 @ emptyset )
=> ( X2 = emptyset ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( ~ ( subset @ X2 @ emptyset )
| ( X2 = emptyset ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl16,plain,
! [X2: $i] :
( ~ ( subset @ X2 @ emptyset )
| ( X2 = emptyset ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl120,plain,
'#sk2' = emptyset,
inference('sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl16]) ).
thf(zip_derived_cl125,plain,
! [X0: $i] :
~ ( in @ X0 @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl93,zip_derived_cl120]) ).
thf(zip_derived_cl36_012,plain,
( ~ '#form6'
| ( '#sk2' != emptyset )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ~ '#form4' ),
inference(renaming,[status(thm)],[zip_derived_cl30,zip_derived_cl32]) ).
thf(zip_derived_cl44_013,plain,
( '#form8'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ emptyset )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ emptyset )
=> ( ( ( in @ Y1 @ Y2 )
& ( in @ Y0 @ Y1 ) )
=> ( in @ Y0 @ Y2 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl46,plain,
( ~ '#form8'
| ~ '#form4'
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ emptyset )
=> ( (~) @ ( in @ Y0 @ Y0 ) ) ) )
| ( '#sk2' != emptyset )
| ~ '#form6' ),
inference(renaming,[status(thm)],[zip_derived_cl36,zip_derived_cl44]) ).
thf(zip_derived_cl51,plain,
( ~ ( ( in @ '#sk3' @ emptyset )
=> ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
| ~ '#form6'
| ( '#sk2' != emptyset )
| ~ '#form4'
| ~ '#form8' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl57,plain,
( ~ ( ( in @ '#sk3' @ '#sk2' )
=> ( (~) @ ( in @ '#sk3' @ '#sk3' ) ) )
| ~ '#form6'
| ( '#sk2' != emptyset )
| ~ '#form4'
| ~ '#form8' ),
inference(local_rewriting,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl58,plain,
( ( in @ '#sk3' @ '#sk2' )
| ~ '#form8'
| ~ '#form4'
| ( '#sk2' != emptyset )
| ~ '#form6' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl100_014,plain,
'#form8',
inference(clc,[status(thm)],[zip_derived_cl52,zip_derived_cl93]) ).
thf(zip_derived_cl98_015,plain,
'#form4',
inference(clc,[status(thm)],[zip_derived_cl37,zip_derived_cl93]) ).
thf(zip_derived_cl99_016,plain,
'#form6',
inference(clc,[status(thm)],[zip_derived_cl41,zip_derived_cl93]) ).
thf(zip_derived_cl113,plain,
( ( in @ '#sk3' @ '#sk2' )
| ( '#sk2' != emptyset ) ),
inference(demod,[status(thm)],[zip_derived_cl58,zip_derived_cl100,zip_derived_cl98,zip_derived_cl99]) ).
thf(zip_derived_cl120_017,plain,
'#sk2' = emptyset,
inference('sup-',[status(thm)],[zip_derived_cl116,zip_derived_cl16]) ).
thf(zip_derived_cl126,plain,
( ( in @ '#sk3' @ '#sk2' )
| ( '#sk2' != '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl113,zip_derived_cl120]) ).
thf(zip_derived_cl127,plain,
in @ '#sk3' @ '#sk2',
inference(simplify,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl132,plain,
$false,
inference('sup+',[status(thm)],[zip_derived_cl125,zip_derived_cl127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU820^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.KNnaiN1CJS true
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 19:26:52 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.35 % Running portfolio for 300 s
% 0.20/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % Number of cores: 8
% 0.20/0.35 % Python version: Python 3.6.8
% 0.20/0.35 % Running in HO mode
% 0.21/0.64 % Total configuration time : 828
% 0.21/0.64 % Estimated wc time : 1656
% 0.21/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 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/20_acsne_simpl.sh running for 40s
% 0.21/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.48/0.84 % Solved by lams/35_full_unif4.sh.
% 1.48/0.84 % done 23 iterations in 0.059s
% 1.48/0.84 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.48/0.84 % SZS output start Refutation
% See solution above
% 1.48/0.84
% 1.48/0.84
% 1.48/0.84 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.48/0.84 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.48/0.84 % Terminating...
% 1.95/0.94 % Runner terminated.
% 1.95/0.95 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------