%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU789^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1fIUxdqhuy true
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 04:56:23 PM UTC 2025
% Result : Theorem 1.32s 1.08s
% Output : Refutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 108 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 739 ( 39 equ; 0 cnn)
% Maximal formula atoms : 43 ( 6 avg)
% Number of connectives : 3156 ( 229 ~; 228 |; 0 &;2316 @)
% ( 0 <=>; 261 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-3 aty)
% ( 122 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 402 ( 122 ^; 280 !; 0 ?; 402 :)
% Comments :
%------------------------------------------------------------------------------
thf(breln1invset_type,type,
breln1invset: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(setextsub_type,type,
setextsub: $o ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(subbreln1_type,type,
subbreln1: $o ).
thf('#sk3_type',type,
'#sk3': $i > $i > $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(breln1invE_type,type,
breln1invE: $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(breln1invI_type,type,
breln1invI: $o ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i > $i ).
thf(breln1invprop_type,type,
breln1invprop: $o ).
thf(breln1invE,axiom,
( breln1invE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ) ).
thf('0',plain,
( breln1invE
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) )
=> ( in @ ( kpair @ X8 @ X10 ) @ X6 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1invI,axiom,
( breln1invI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ).
thf('1',plain,
( breln1invI
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( ( in @ ( kpair @ X8 @ X10 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X8 ) @ ( breln1invset @ X4 @ X6 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(breln1invprop,axiom,
( breln1invprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ) ).
thf('2',plain,
( breln1invprop
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ( breln1 @ X4 @ ( breln1invset @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
thf(subbreln1,axiom,
( subbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ) ).
thf('3',plain,
( subbreln1
= ( ! [X4: $i,X6: $i] :
( ( breln1 @ X4 @ X6 )
=> ! [X8: $i] :
( ( breln1 @ X4 @ X8 )
=> ( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ( ( in @ ( kpair @ X10 @ X12 ) @ X6 )
=> ( in @ ( kpair @ X10 @ X12 ) @ X8 ) ) ) )
=> ( subset @ X6 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(setextsub,axiom,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf('4',plain,
( setextsub
= ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X4 )
=> ( X4 = X6 ) ) ) ) ),
define([status(thm)]) ).
thf(woz2Ex,conjecture,
( setextsub
=> ( subbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X4 )
=> ( X4 = X6 ) ) )
=> ( ! [X8: $i,X10: $i] :
( ( breln1 @ X8 @ X10 )
=> ! [X12: $i] :
( ( breln1 @ X8 @ X12 )
=> ( ! [X14: $i] :
( ( in @ X14 @ X8 )
=> ! [X16: $i] :
( ( in @ X16 @ X8 )
=> ( ( in @ ( kpair @ X14 @ X16 ) @ X10 )
=> ( in @ ( kpair @ X14 @ X16 ) @ X12 ) ) ) )
=> ( subset @ X10 @ X12 ) ) ) )
=> ( ! [X18: $i,X20: $i] :
( ( breln1 @ X18 @ X20 )
=> ( breln1 @ X18 @ ( breln1invset @ X18 @ X20 ) ) )
=> ( ! [X22: $i,X24: $i] :
( ( breln1 @ X22 @ X24 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X28: $i] :
( ( in @ X28 @ X22 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X24 )
=> ( in @ ( kpair @ X28 @ X26 ) @ ( breln1invset @ X22 @ X24 ) ) ) ) ) )
=> ( ! [X30: $i,X32: $i] :
( ( breln1 @ X30 @ X32 )
=> ! [X34: $i] :
( ( in @ X34 @ X30 )
=> ! [X36: $i] :
( ( in @ X36 @ X30 )
=> ( ( in @ ( kpair @ X36 @ X34 ) @ ( breln1invset @ X30 @ X32 ) )
=> ( in @ ( kpair @ X34 @ X36 ) @ X32 ) ) ) ) )
=> ! [X38: $i,X40: $i] :
( ( breln1 @ X38 @ X40 )
=> ( X40
= ( breln1invset @ X38 @ ( breln1invset @ X38 @ X40 ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i] :
( ( subset @ X4 @ X6 )
=> ( ( subset @ X6 @ X4 )
=> ( X4 = X6 ) ) )
=> ( ! [X8: $i,X10: $i] :
( ( breln1 @ X8 @ X10 )
=> ! [X12: $i] :
( ( breln1 @ X8 @ X12 )
=> ( ! [X14: $i] :
( ( in @ X14 @ X8 )
=> ! [X16: $i] :
( ( in @ X16 @ X8 )
=> ( ( in @ ( kpair @ X14 @ X16 ) @ X10 )
=> ( in @ ( kpair @ X14 @ X16 ) @ X12 ) ) ) )
=> ( subset @ X10 @ X12 ) ) ) )
=> ( ! [X18: $i,X20: $i] :
( ( breln1 @ X18 @ X20 )
=> ( breln1 @ X18 @ ( breln1invset @ X18 @ X20 ) ) )
=> ( ! [X22: $i,X24: $i] :
( ( breln1 @ X22 @ X24 )
=> ! [X26: $i] :
( ( in @ X26 @ X22 )
=> ! [X28: $i] :
( ( in @ X28 @ X22 )
=> ( ( in @ ( kpair @ X26 @ X28 ) @ X24 )
=> ( in @ ( kpair @ X28 @ X26 ) @ ( breln1invset @ X22 @ X24 ) ) ) ) ) )
=> ( ! [X30: $i,X32: $i] :
( ( breln1 @ X30 @ X32 )
=> ! [X34: $i] :
( ( in @ X34 @ X30 )
=> ! [X36: $i] :
( ( in @ X36 @ X30 )
=> ( ( in @ ( kpair @ X36 @ X34 ) @ ( breln1invset @ X30 @ X32 ) )
=> ( in @ ( kpair @ X34 @ X36 ) @ X32 ) ) ) ) )
=> ! [X38: $i,X40: $i] :
( ( breln1 @ X38 @ X40 )
=> ( X40
= ( breln1invset @ X38 @ ( breln1invset @ X38 @ X40 ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y0 = Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( breln1 @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ( breln1 @ X2 @ X4 )
=> ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( breln1 @ Y0 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( breln1 @ X2 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i] :
( ( breln1 @ X2 @ X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X4 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X4 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X4 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X4 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( breln1 @ X2 @ X6 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X4 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X6 ) ) ) ) ) )
=> ( subset @ X4 @ X6 ) ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( breln1 @ X2 @ X6 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X4 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X6 ) ) ) ) ) )
=> ( subset @ X4 @ X6 ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X4 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X6 ) ) ) ) ) )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk3' @ X2 @ X4 @ X6 ) @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) @ X4 )
=> ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) ) )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk3' @ X2 @ X4 @ X6 ) @ X2 )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) @ X4 )
=> ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ Y0 ) @ X6 ) ) ) )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X4 )
=> ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X6 ) ) )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X4 )
=> ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X6 ) )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X4 )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl9,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ X2 @ Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ( breln1 @ X2 @ X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X4 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X4 )
=> ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X6 @ Y0 ) @ X4 )
=> ( in @ ( kpair @ Y0 @ X6 ) @ ( breln1invset @ X2 @ X4 ) ) ) ) ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X6 @ Y0 ) @ X4 )
=> ( in @ ( kpair @ Y0 @ X6 ) @ ( breln1invset @ X2 @ X4 ) ) ) ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( in @ ( kpair @ X6 @ X8 ) @ X4 )
=> ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) ) ) )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( in @ ( kpair @ X6 @ X8 ) @ X4 )
=> ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) ) )
| ~ ( in @ X6 @ X2 )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ ( kpair @ X6 @ X8 ) @ X4 )
| ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X6 )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk3' @ X3 @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X1 )
| ~ ( in @ ( '#sk4' @ X3 @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( in @ ( kpair @ ( '#sk4' @ X3 @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ ( '#sk3' @ X3 @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X0 )
| ( subset @ X2 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( breln1 @ X3 @ X2 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl52]) ).
thf(zip_derived_cl49_001,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ ( kpair @ X6 @ X8 ) @ X4 )
| ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( breln1 @ X4 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X4 @ X3 )
| ( subset @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( '#sk3' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ ( '#sk3' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( in @ ( kpair @ ( '#sk3' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ ( '#sk4' @ X4 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) ) @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl57,zip_derived_cl49]) ).
thf(zip_derived_cl135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subset @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X3 @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( in @ ( '#sk3' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ ( '#sk4' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ ( '#sk3' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( '#sk4' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ X0 ) )
| ( subset @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X3 @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl88]) ).
thf(zip_derived_cl140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( '#sk3' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( '#sk4' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ ( '#sk3' @ X3 @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X3 @ X0 )
| ( subset @ X0 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( in @ ( '#sk3' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ ( '#sk4' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ ( '#sk3' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
| ~ ( in @ ( '#sk4' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ ( '#sk3' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 )
| ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl23_002,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl152,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( in @ ( '#sk3' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ ( '#sk4' @ X2 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl146,zip_derived_cl23]) ).
thf(zip_derived_cl153,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( in @ ( '#sk4' @ X0 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl152]) ).
thf(zip_derived_cl155,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk4' @ X0 @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) @ X0 )
| ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl157,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 )
| ( subset @ X1 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl155,zip_derived_cl47]) ).
thf(zip_derived_cl158,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) )
| ( subset @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl157]) ).
thf(zip_derived_cl23_003,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl160,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ X0 )
| ( subset @ X0 @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl158,zip_derived_cl23]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 )
=> ( ( subset @ Y1 @ Y0 )
=> ( Y0 = Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( subset @ X2 @ Y0 )
=> ( ( subset @ Y0 @ X2 )
=> ( X2 = Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i] :
( ( subset @ X2 @ X4 )
=> ( ( subset @ X4 @ X2 )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i] :
( ~ ( subset @ X2 @ X4 )
| ( ( subset @ X4 @ X2 )
=> ( X2 = X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i] :
( ~ ( subset @ X4 @ X2 )
| ( X2 = X4 )
| ~ ( subset @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i] :
( ~ ( subset @ X4 @ X2 )
| ( X2 = X4 )
| ~ ( subset @ X2 @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl161,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ X0 )
| ~ ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
| ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl160,zip_derived_cl21]) ).
thf(zip_derived_cl23_004,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl40_005,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk3' @ X2 @ X4 @ X6 ) @ X2 )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl52_006,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X6 )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl51_007,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( kpair @ ( '#sk3' @ X2 @ X4 @ X6 ) @ ( '#sk4' @ X2 @ X4 @ X6 ) ) @ X4 )
| ~ ( breln1 @ X2 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ( subset @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl14,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl19,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y2 ) @ ( breln1invset @ Y0 @ Y1 ) )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( breln1 @ X2 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y2 @ Y1 ) @ ( breln1invset @ X2 @ Y0 ) )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ( breln1 @ X2 @ X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y0 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X4 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ X6 @ Y0 ) @ X4 ) ) ) ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ X6 @ Y0 ) @ X4 ) ) ) )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ X6 @ X8 ) @ X4 ) ) )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
=> ( in @ ( kpair @ X6 @ X8 ) @ X4 ) )
| ~ ( in @ X6 @ X2 )
| ~ ( breln1 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
| ( in @ ( kpair @ X6 @ X8 ) @ X4 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subset @ ( breln1invset @ X1 @ X0 ) @ X2 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( breln1 @ X3 @ X2 )
| ~ ( in @ ( '#sk3' @ X3 @ ( breln1invset @ X1 @ X0 ) @ X2 ) @ X1 )
| ~ ( in @ ( '#sk4' @ X3 @ ( breln1invset @ X1 @ X0 ) @ X2 ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ( in @ ( kpair @ ( '#sk4' @ X3 @ ( breln1invset @ X1 @ X0 ) @ X2 ) @ ( '#sk3' @ X3 @ ( breln1invset @ X1 @ X0 ) @ X2 ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl53]) ).
thf(zip_derived_cl53_008,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ ( kpair @ X8 @ X6 ) @ ( breln1invset @ X2 @ X4 ) )
| ( in @ ( kpair @ X6 @ X8 ) @ X4 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( in @ X6 @ X2 )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( breln1 @ X3 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X3 )
| ~ ( in @ ( '#sk3' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X3 )
| ~ ( breln1 @ X4 @ X2 )
| ~ ( breln1 @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) )
| ( subset @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 )
| ~ ( in @ ( '#sk4' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 )
| ~ ( in @ ( '#sk3' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ( in @ ( kpair @ ( '#sk3' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) @ ( '#sk4' @ X4 @ ( breln1invset @ X3 @ ( breln1invset @ X1 @ X0 ) ) @ X2 ) ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl53]) ).
thf(zip_derived_cl189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subset @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X3 @ X0 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( in @ ( '#sk3' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X1 )
| ~ ( in @ ( '#sk4' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X1 )
| ( subset @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ~ ( breln1 @ X3 @ X0 )
| ~ ( in @ ( '#sk3' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X2 )
| ~ ( in @ ( '#sk4' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X2 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl52,zip_derived_cl94]) ).
thf(zip_derived_cl197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( breln1 @ X2 @ ( breln1invset @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X2 )
| ~ ( in @ ( '#sk3' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X2 )
| ~ ( in @ ( '#sk4' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X1 )
| ~ ( in @ ( '#sk3' @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) @ X1 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( breln1 @ X3 @ X0 )
| ~ ( breln1 @ X3 @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) )
| ( subset @ ( breln1invset @ X2 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( in @ ( '#sk3' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( in @ ( '#sk4' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( in @ ( '#sk3' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ X1 ) )
| ~ ( in @ ( '#sk4' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( in @ ( '#sk3' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl23_009,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
| ~ ( breln1 @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X2 @ X1 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( in @ ( '#sk3' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( in @ ( '#sk4' @ X2 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl206,zip_derived_cl23]) ).
thf(zip_derived_cl213,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
| ~ ( in @ ( '#sk4' @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl40,zip_derived_cl212]) ).
thf(zip_derived_cl215,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk4' @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) @ X0 )
| ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ~ ( breln1 @ X0 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl213]) ).
thf(zip_derived_cl47_010,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ( subset @ X4 @ X6 )
| ~ ( breln1 @ X2 @ X4 )
| ~ ( breln1 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl217,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X0 @ X1 )
| ~ ( breln1 @ X0 @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) )
| ( subset @ ( breln1invset @ X0 @ ( breln1invset @ X0 @ X1 ) ) @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl215,zip_derived_cl47]) ).
thf(zip_derived_cl218,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ ( breln1invset @ X1 @ X0 ) )
| ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 )
| ~ ( breln1 @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl217]) ).
thf(zip_derived_cl23_011,plain,
! [X2: $i,X4: $i] :
( ~ ( breln1 @ X2 @ X4 )
| ( breln1 @ X2 @ ( breln1invset @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl220,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ X0 )
| ( subset @ ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) ) @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl218,zip_derived_cl23]) ).
thf(zip_derived_cl223,plain,
! [X0: $i,X1: $i] :
( ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 )
| ~ ( breln1 @ X1 @ X0 )
| ~ ( breln1 @ X1 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl161,zip_derived_cl220]) ).
thf(zip_derived_cl227,plain,
! [X0: $i,X1: $i] :
( ~ ( breln1 @ X1 @ X0 )
| ( ( breln1invset @ X1 @ ( breln1invset @ X1 @ X0 ) )
= X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl223]) ).
thf(zip_derived_cl20,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( breln1 @ Y0 @ Y1 )
=> ( Y1
= ( breln1invset @ Y0 @ ( breln1invset @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl26,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( breln1 @ '#sk1' @ Y0 )
=> ( Y0
= ( breln1invset @ '#sk1' @ ( breln1invset @ '#sk1' @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl30,plain,
~ ( ( breln1 @ '#sk1' @ '#sk2' )
=> ( '#sk2'
= ( breln1invset @ '#sk1' @ ( breln1invset @ '#sk1' @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl35,plain,
( '#sk2'
!= ( breln1invset @ '#sk1' @ ( breln1invset @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl39,plain,
( '#sk2'
!= ( breln1invset @ '#sk1' @ ( breln1invset @ '#sk1' @ '#sk2' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl231,plain,
( ( '#sk2' != '#sk2' )
| ~ ( breln1 @ '#sk1' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl227,zip_derived_cl39]) ).
thf(zip_derived_cl34,plain,
breln1 @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl288,plain,
'#sk2' != '#sk2',
inference(demod,[status(thm)],[zip_derived_cl231,zip_derived_cl34]) ).
thf(zip_derived_cl289,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU789^2 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1fIUxdqhuy true
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 16:03:38 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.18/0.61 % Total configuration time : 828
% 0.18/0.61 % Estimated wc time : 1656
% 0.18/0.61 % Estimated cpu time (8 cpus) : 207.0
% 0.87/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.87/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.87/0.70 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.87/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.29/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.29/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.29/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.29/0.72 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 1.32/1.08 % Solved by lams/30_sp5.sh.
% 1.32/1.08 % done 60 iterations in 0.282s
% 1.32/1.08 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.32/1.08 % SZS output start Refutation
% See solution above
% 1.32/1.08
% 1.32/1.08
% 1.32/1.08 % Terminating...
% 1.32/1.14 % Runner terminated.
% 1.84/1.16 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------