TSTP Solution File: SEU753^2 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU753^2 : 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.CSgmGUHGCh true
% Computer : n005.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 19:17:03 EDT 2023
% Result : Theorem 8.67s 1.77s
% Output : Refutation 8.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 27
% Syntax : Number of formulae : 164 ( 12 unt; 20 typ; 0 def)
% Number of atoms : 1066 ( 92 equ; 144 cnn)
% Maximal formula atoms : 22 ( 7 avg)
% Number of connectives : 5773 ( 309 ~; 340 |; 0 &;4686 @)
% ( 6 <=>; 287 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 20 usr; 14 con; 0-6 aty)
% ( 145 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 370 ( 45 ^; 313 !; 0 ?; 370 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(setextT_type,type,
setextT: $o ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(binunionT_lem_type,type,
binunionT_lem: $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(binintersectT_lem_type,type,
binintersectT_lem: $o ).
thf(binintersect_type,type,
binintersect: $i > $i > $i ).
thf(demorgan1a_type,type,
demorgan1a: $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(demorgan1b_type,type,
demorgan1b: $o ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i > $i ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(demorgan1,conjecture,
( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[demorgan1]) ).
thf(zip_derived_cl0,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) )
= ( binunion @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( binintersectT_lem
=> ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
~ ( binunionT_lem
=> ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( complementT_lem
=> ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl11,plain,
~ ( setextT
=> ( demorgan1a
=> ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl16,plain,
setextT,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(setextT,axiom,
( setextT
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) )
= $true ) ) ).
thf('0',plain,
( setextT
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ( ! [X11: $i] :
( ( in @ X11 @ X5 )
=> ( ( in @ X11 @ X7 )
=> ( in @ X11 @ X9 ) ) )
=> ( ! [X13: $i] :
( ( in @ X13 @ X5 )
=> ( ( in @ X13 @ X9 )
=> ( in @ X13 @ X7 ) ) )
=> ( X7 = X9 ) ) ) ) ) ),
inference('rw.lit',[status(esa)],[setextT]) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y1 )
=> ( in @ Y3 @ Y2 ) ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ Y2 )
=> ( in @ Y3 @ Y1 ) ) ) )
=> ( Y1 = Y2 ) ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl16,'0']) ).
thf(zip_derived_cl28,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) ) @ (=) ) ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) @ ( '#C' @ in ) ) ) ) ) ) @ (=) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) @ ( '#C' @ in @ X4 ) ) ) ) ) @ ( $i = X4 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) @ ( '#C' @ in @ X4 ) ) ) ) ) @ ( $i = X4 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
=> ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
=> ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
=> ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl69,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl74,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X2 )
=> ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl80,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) )
| ( X4 = X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl17,plain,
~ ( demorgan1a
=> ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl23,plain,
demorgan1a,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(demorgan1a,axiom,
( demorgan1a
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ) ) ).
thf('1',plain,
( demorgan1a
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ! [X11: $i] :
( ( in @ X11 @ X5 )
=> ( ( in @ X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) )
=> ( in @ X11 @ ( binunion @ ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) ) ) ) ) ) ),
inference('rw.lit',[status(esa)],[demorgan1a]) ).
thf(zip_derived_cl30,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( binunion @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl23,'1']) ).
thf(zip_derived_cl37,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl38,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#B' @ ( '#B' @ ( setminus @ X2 ) ) @ binintersect ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ binunion @ ( setminus @ X2 ) ) ) @ ( setminus @ X2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( binunion @ ( setminus @ X2 @ X4 ) ) @ ( setminus @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( binunion @ ( setminus @ X2 @ X4 ) ) @ ( setminus @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl53,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) @ ( '#C' @ in @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) @ ( '#C' @ in @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
=> ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
=> ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) )
= X3 )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X4 )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl86,zip_derived_cl72]) ).
thf(zip_derived_cl476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X3 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X3 )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl85,zip_derived_cl103]) ).
thf(zip_derived_cl493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X3 )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl476]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
=> ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X2 )
=> ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) ) )
| ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl94,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 )
| ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl72_001,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) )
= X3 )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X3 )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl94,zip_derived_cl72]) ).
thf(zip_derived_cl72_002,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
=> ( X4 = X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl81,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X6 ) ) @ ( '#C' @ in @ X4 ) ) ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X2 )
=> ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl88,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
=> ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 ) )
| ( X4 = X6 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl92,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl24,plain,
~ ( demorgan1b
=> ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl31,plain,
demorgan1b,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(demorgan1b,axiom,
( demorgan1b
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) )
= $true ) ) ).
thf('2',plain,
( demorgan1b
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ! [X11: $i] :
( ( in @ X11 @ X5 )
=> ( ( in @ X11 @ ( binunion @ ( setminus @ X5 @ X7 ) @ ( setminus @ X5 @ X9 ) ) )
=> ( in @ X11 @ ( setminus @ X5 @ ( binintersect @ X7 @ X9 ) ) ) ) ) ) ) ),
inference('rw.lit',[status(esa)],[demorgan1b]) ).
thf(zip_derived_cl39,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ ( binunion @ ( setminus @ Y0 @ Y1 ) @ ( setminus @ Y0 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y0 @ ( binintersect @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl31,'2']) ).
thf(zip_derived_cl44,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#C' @ in ) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ binunion @ ( setminus @ X2 ) ) ) @ ( setminus @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#B' @ ( '#B' @ ( setminus @ X2 ) ) @ binintersect ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( binunion @ ( setminus @ X2 @ X4 ) ) @ ( setminus @ X2 ) ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( binunion @ ( setminus @ X2 @ X4 ) ) @ ( setminus @ X2 ) ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binintersect @ X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
=> ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl73,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
=> ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) )
= X3 )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl92,zip_derived_cl78]) ).
thf(zip_derived_cl419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X1 )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) )
= X3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl133]) ).
thf(zip_derived_cl428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) )
= X3 )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X1 )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl419]) ).
thf(zip_derived_cl1082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl95,zip_derived_cl428]) ).
thf(zip_derived_cl1098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1082]) ).
thf(zip_derived_cl92_003,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl91,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl78_004,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3
= ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X3 )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl78]) ).
thf(zip_derived_cl1018,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl92,zip_derived_cl259]) ).
thf(zip_derived_cl1033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1018]) ).
thf(zip_derived_cl1123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X2 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) )
= ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl1098,zip_derived_cl1033]) ).
thf(zip_derived_cl1132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl493,zip_derived_cl1123]) ).
thf(zip_derived_cl1136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl1132]) ).
thf(zip_derived_cl79,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X2 )
| ( X4 = X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl86_005,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X4 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl85_006,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X6 @ X4 ) @ X6 )
| ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( X4 = X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl78_007,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( binunion @ ( setminus @ X2 @ X4 ) @ ( setminus @ X2 @ X6 ) ) )
| ( in @ X8 @ ( setminus @ X2 @ ( binintersect @ X4 @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X3
= ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ( in @ ( '#sk4' @ X4 @ X3 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) ) @ X4 )
| ~ ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ X1 )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ( in @ ( '#sk4' @ X4 @ ( binunion @ ( setminus @ X1 @ X2 ) @ ( setminus @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl85,zip_derived_cl78]) ).
thf(zip_derived_cl700,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X3 )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X3 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl86,zip_derived_cl211]) ).
thf(zip_derived_cl721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X3 @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) @ X3 )
| ~ ( in @ ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) @ ( powerset @ X3 ) )
| ( ( setminus @ X2 @ ( binintersect @ X1 @ X0 ) )
= ( binunion @ ( setminus @ X2 @ X1 ) @ ( setminus @ X2 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl700]) ).
thf(zip_derived_cl756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ( ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) )
= ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl721]) ).
thf(zip_derived_cl766,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ( in @ ( '#sk4' @ X0 @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) ) @ X0 )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl756]) ).
thf(zip_derived_cl1142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1136,zip_derived_cl766]) ).
thf(zip_derived_cl5,plain,
binunionT_lem,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(binunionT_lem,axiom,
( binunionT_lem
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
= $true ) ) ).
thf('3',plain,
( binunionT_lem
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ( in @ ( binunion @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ),
inference('rw.lit',[status(esa)],[binunionT_lem]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binunion @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl5,'3']) ).
thf(zip_derived_cl13,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binunion ) ) ) @ powerset ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binunion ) ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binunion @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binunion @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( in @ ( binunion @ X4 @ X6 ) @ ( powerset @ X2 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( in @ ( binunion @ X4 @ X6 ) @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl1143,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ X2 ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1142,zip_derived_cl41]) ).
thf(zip_derived_cl10,plain,
complementT_lem,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(complementT_lem,axiom,
( complementT_lem
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ) ) ).
thf('4',plain,
( complementT_lem
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ( in @ ( setminus @ X5 @ X7 ) @ ( powerset @ X5 ) ) ) ),
inference('rw.lit',[status(esa)],[complementT_lem]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl10,'4']) ).
thf(zip_derived_cl20,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ setminus ) ) @ powerset ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( setminus @ X2 ) ) @ ( powerset @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl1145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1143,zip_derived_cl35]) ).
thf(zip_derived_cl35_008,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl1146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1145,zip_derived_cl35]) ).
thf(zip_derived_cl35_009,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl1147,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ ( binintersect @ X2 @ X1 ) @ ( powerset @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl1146,zip_derived_cl35]) ).
thf(zip_derived_cl2,plain,
binintersectT_lem,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(binintersectT_lem,axiom,
( binintersectT_lem
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) )
= $true ) ) ).
thf('5',plain,
( binintersectT_lem
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ( in @ ( binintersect @ X7 @ X9 ) @ ( powerset @ X5 ) ) ) ) ),
inference('rw.lit',[status(esa)],[binintersectT_lem]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( binintersect @ Y1 @ Y2 ) @ ( powerset @ Y0 ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl2,'5']) ).
thf(zip_derived_cl7,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binintersect ) ) ) @ powerset ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ binintersect ) ) @ ( powerset @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binintersect @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( binintersect @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( in @ ( binintersect @ X4 @ X6 ) @ ( powerset @ X2 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( in @ ( binintersect @ X4 @ X6 ) @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl1149,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) )
| ( ( binunion @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= ( setminus @ X0 @ ( binintersect @ X2 @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1147,zip_derived_cl33]) ).
thf(zip_derived_cl32,plain,
~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binintersect ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ binunion ) @ setminus ) ) ) @ setminus ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl40,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=) ) @ ( '#B' @ ( '#B' @ ( setminus @ '#sk1' ) ) @ binintersect ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ binunion @ ( setminus @ '#sk1' ) ) ) @ ( setminus @ '#sk1' ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl46,plain,
~ ( ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binintersect @ '#sk2' ) ) ) @ ( '#B' @ ( binunion @ ( setminus @ '#sk1' @ '#sk2' ) ) @ ( setminus @ '#sk1' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl51,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#S' @ ( '#B' @ (=) @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binintersect @ '#sk2' ) ) ) @ ( '#B' @ ( binunion @ ( setminus @ '#sk1' @ '#sk2' ) ) @ ( setminus @ '#sk1' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl55,plain,
~ ( ( in @ '#sk3' @ ( powerset @ '#sk1' ) )
=> ( ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) )
= ( binunion @ ( setminus @ '#sk1' @ '#sk2' ) @ ( setminus @ '#sk1' @ '#sk3' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl60,plain,
( ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) )
!= ( binunion @ ( setminus @ '#sk1' @ '#sk2' ) @ ( setminus @ '#sk1' @ '#sk3' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl64,plain,
( ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) )
!= ( binunion @ ( setminus @ '#sk1' @ '#sk2' ) @ ( setminus @ '#sk1' @ '#sk3' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl1180,plain,
( ( ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) )
!= ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) )
| ~ ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
| ~ ( in @ '#sk3' @ ( powerset @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1149,zip_derived_cl64]) ).
thf(zip_derived_cl50,plain,
in @ '#sk2' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl59,plain,
in @ '#sk3' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl1210,plain,
( ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) )
!= ( setminus @ '#sk1' @ ( binintersect @ '#sk2' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1180,zip_derived_cl50,zip_derived_cl59]) ).
thf(zip_derived_cl1211,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl1210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU753^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.CSgmGUHGCh true
% 0.15/0.37 % Computer : n005.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Aug 23 16:27:23 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.38 % Running in HO mode
% 0.24/0.65 % Total configuration time : 828
% 0.24/0.65 % Estimated wc time : 1656
% 0.24/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.24/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.24/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.24/0.79 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.24/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.24/0.79 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.24/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.24/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.23/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 8.67/1.77 % Solved by lams/40_b.comb.sh.
% 8.67/1.77 % done 145 iterations in 0.934s
% 8.67/1.77 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 8.67/1.77 % SZS output start Refutation
% See solution above
% 8.67/1.78
% 8.67/1.78
% 8.67/1.78 % Terminating...
% 9.39/1.89 % Runner terminated.
% 9.39/1.89 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------