%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU749^2 : 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.OmG8mY3pzq true
% Computer : n031.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 04:56:06 PM UTC 2025
% Result : Theorem 17.02s 2.70s
% Output : Refutation 17.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 76 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 463 ( 4 equ; 64 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 2082 ( 88 ~; 77 |; 0 &;1679 @)
% ( 4 <=>; 149 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 11 con; 0-6 aty)
% ( 85 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 140 ( 29 ^; 111 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(binunionT_lem_type,type,
binunionT_lem: $o ).
thf(powersetTI1_type,type,
powersetTI1: $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(complementT_lem_type,type,
complementT_lem: $o ).
thf(demorgan2a1_type,type,
demorgan2a1: $o ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i > $i ).
thf(setminus_type,type,
setminus: $i > $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf('#sk1_type',type,
'#sk1': $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(complementUnionInPowersetComplement,conjecture,
( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[complementUnionInPowersetComplement]) ).
thf(zip_derived_cl0,plain,
~ ( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ ( binunion @ Y1 @ Y2 ) ) @ ( powerset @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( binunionT_lem
=> ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ( !! @ ( '#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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) @ ( '#B' @ ( '#B' @ powerset ) @ setminus ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
binunionT_lem,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
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('0',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_cl4,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_cl2,'0']) ).
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 ) @ binunion ) ) ) @ 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 ) @ binunion ) ) @ ( 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 @ ( binunion @ 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 @ ( binunion @ X4 ) ) @ ( powerset @ X2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl24,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_cl18]) ).
thf(zip_derived_cl30,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_cl24]) ).
thf(zip_derived_cl3,plain,
~ ( complementT_lem
=> ( powersetTI1
=> ( demorgan2a1
=> ( !! @ ( '#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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) @ ( '#B' @ ( '#B' @ powerset ) @ setminus ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
~ ( powersetTI1
=> ( demorgan2a1
=> ( !! @ ( '#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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) @ ( '#B' @ ( '#B' @ powerset ) @ setminus ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl11,plain,
~ ( demorgan2a1
=> ( !! @ ( '#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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) @ ( '#B' @ ( '#B' @ powerset ) @ setminus ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl17,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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ in ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) @ ( '#B' @ ( '#B' @ powerset ) @ setminus ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl23,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ ( '#B' @ ( '#B' @ ( setminus @ '#sk1' ) ) @ binunion ) ) ) @ ( '#B' @ powerset @ ( setminus @ '#sk1' ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl29,plain,
~ ( ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#C' @ ( '#B' @ in @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binunion @ '#sk2' ) ) ) @ ( powerset @ ( setminus @ '#sk1' @ '#sk2' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl34,plain,
~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ '#sk1' ) ) ) @ ( '#C' @ ( '#B' @ in @ ( '#B' @ ( setminus @ '#sk1' ) @ ( binunion @ '#sk2' ) ) ) @ ( powerset @ ( setminus @ '#sk1' @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl37,plain,
~ ( ( in @ '#sk3' @ ( powerset @ '#sk1' ) )
=> ( in @ ( setminus @ '#sk1' @ ( binunion @ '#sk2' @ '#sk3' ) ) @ ( powerset @ ( setminus @ '#sk1' @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl41,plain,
~ ( in @ ( setminus @ '#sk1' @ ( binunion @ '#sk2' @ '#sk3' ) ) @ ( powerset @ ( setminus @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl10,plain,
powersetTI1,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(powersetTI1,axiom,
( powersetTI1
=> ( ( !!
@ ^ [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 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) )
= $true ) ) ).
thf('1',plain,
( powersetTI1
<=> ! [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 ) ) )
=> ( in @ X7 @ ( powerset @ X9 ) ) ) ) ) ),
inference('rw.lit',[status(esa)],[powersetTI1]) ).
thf(zip_derived_cl15,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 ) ) ) )
=> ( in @ Y1 @ ( powerset @ Y2 ) ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl10,'1']) ).
thf(zip_derived_cl20,plain,
!! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ powerset ) ) ) ) @ ( '#C' @ ( '#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' @ '#B' @ in ) @ powerset ) ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,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 ) ) ) ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ in ) @ powerset ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl26,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 ) ) ) ) ) @ ( '#B' @ ( in @ X4 ) @ powerset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl31,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 ) ) ) ) ) @ ( '#B' @ ( in @ X4 ) @ powerset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
=> ( in @ X4 @ ( powerset @ X6 ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
=> ( in @ X4 @ ( powerset @ X6 ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X4 ) ) @ ( '#C' @ in @ X6 ) ) ) )
| ( in @ X4 @ ( powerset @ X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl44,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 ) )
| ( in @ X4 @ ( powerset @ X6 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X2 )
| ( in @ X4 @ ( powerset @ X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
=> ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 ) )
| ( in @ X4 @ ( powerset @ X6 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X6 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ X4 @ ( powerset @ X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 ) @ X4 )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ X4 @ ( powerset @ X6 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl16,plain,
demorgan2a1,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(demorgan2a1,axiom,
( demorgan2a1
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( powerset @ Y0 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ Y3 @ ( setminus @ Y0 @ ( binunion @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) )
= $true ) ) ).
thf('2',plain,
( demorgan2a1
<=> ! [X5: $i,X7: $i] :
( ( in @ X7 @ ( powerset @ X5 ) )
=> ! [X9: $i] :
( ( in @ X9 @ ( powerset @ X5 ) )
=> ! [X11: $i] :
( ( in @ X11 @ X5 )
=> ( ( in @ X11 @ ( setminus @ X5 @ ( binunion @ X7 @ X9 ) ) )
=> ( in @ X11 @ ( setminus @ X5 @ X7 ) ) ) ) ) ) ),
inference('rw.lit',[status(esa)],[demorgan2a1]) ).
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 @ ( setminus @ Y0 @ ( binunion @ Y1 @ Y2 ) ) )
=> ( in @ Y3 @ ( setminus @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(rw_clause,[status(thm)],[zip_derived_cl16,'2']) ).
thf(zip_derived_cl27,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' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) ) @ ( '#C' @ ( '#B' @ '#B' @ ( '#B' @ '#B' @ setminus ) ) @ binunion ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ setminus ) ) ) ) ) ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl28,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' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#C' @ in ) ) @ ( '#B' @ ( '#B' @ ( setminus @ X2 ) ) @ binunion ) ) ) ) ) @ ( '#B' @ ( '#C' @ in ) @ ( setminus @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binunion @ X4 ) ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) ) ) ) ),
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 ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#C' @ in ) @ ( '#B' @ ( setminus @ X2 ) @ ( binunion @ X4 ) ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ ( powerset @ X2 ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ ( binunion @ X4 @ X6 ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ ( powerset @ X2 ) )
| ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ X2 ) ) @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( setminus @ X2 @ ( binunion @ X4 @ X6 ) ) ) ) @ ( '#C' @ in @ ( setminus @ X2 @ X4 ) ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ X2 )
=> ( ( in @ X8 @ ( setminus @ X2 @ ( binunion @ X4 @ X6 ) ) )
=> ( in @ X8 @ ( setminus @ X2 @ X4 ) ) ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ X2 )
| ( ( in @ X8 @ ( setminus @ X2 @ ( binunion @ X4 @ X6 ) ) )
=> ( in @ X8 @ ( setminus @ X2 @ X4 ) ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ ( setminus @ X2 @ ( binunion @ X4 @ X6 ) ) )
| ( in @ X8 @ ( setminus @ X2 @ X4 ) )
| ~ ( in @ X4 @ ( powerset @ X2 ) )
| ~ ( in @ X6 @ ( powerset @ X2 ) )
| ~ ( in @ X8 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( in @ ( setminus @ X2 @ ( binunion @ X1 @ X0 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X2 @ ( binunion @ X1 @ X0 ) ) @ ( powerset @ X4 ) )
| ~ ( in @ X3 @ ( powerset @ X4 ) )
| ~ ( in @ ( '#sk4' @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X0 ) ) @ X3 ) @ X2 )
| ~ ( in @ X0 @ ( powerset @ X2 ) )
| ~ ( in @ X1 @ ( powerset @ X2 ) )
| ( in @ ( '#sk4' @ X4 @ ( setminus @ X2 @ ( binunion @ X1 @ X0 ) ) @ X3 ) @ ( setminus @ X2 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl51]) ).
thf(zip_derived_cl128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ ( setminus @ X1 @ X0 ) ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( setminus @ X1 @ X0 ) ) @ X1 )
| ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
| ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ ( setminus @ X1 @ X0 ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl50,zip_derived_cl58]) ).
thf(zip_derived_cl130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( '#sk4' @ X3 @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( setminus @ X1 @ X0 ) ) @ X1 )
| ~ ( in @ X2 @ ( powerset @ X1 ) )
| ~ ( in @ X0 @ ( powerset @ X1 ) )
| ~ ( in @ ( setminus @ X1 @ X0 ) @ ( powerset @ X3 ) )
| ~ ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ X3 ) )
| ( in @ ( setminus @ X1 @ ( binunion @ X0 @ X2 ) ) @ ( powerset @ ( setminus @ X1 @ X0 ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl342,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
| ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
| ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl46,zip_derived_cl130]) ).
thf(zip_derived_cl345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X2 @ ( powerset @ X0 ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
| ~ ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
| ~ ( in @ ( setminus @ X0 @ X1 ) @ ( powerset @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl342]) ).
thf(zip_derived_cl5,plain,
complementT_lem,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3]) ).
thf(complementT_lem,axiom,
( complementT_lem
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( powerset @ Y0 ) ) ) ) )
= $true ) ) ).
thf('3',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_cl9,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( powerset @ Y0 ) )
=> ( in @ ( setminus @ Y0 @ Y1 ) @ ( 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 ) ) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ in ) @ setminus ) ) @ powerset ) ) ),
inference('comb-normalize',[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] : ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ in @ ( powerset @ X2 ) ) ) @ ( '#C' @ ( '#B' @ in @ ( setminus @ X2 ) ) @ ( powerset @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X2 ) )
=> ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl351,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ X0 ) )
| ( in @ ( setminus @ X0 @ ( binunion @ X1 @ X2 ) ) @ ( powerset @ ( setminus @ X0 @ X1 ) ) )
| ~ ( in @ X1 @ ( powerset @ X0 ) )
| ~ ( in @ X2 @ ( powerset @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl345,zip_derived_cl25]) ).
thf(zip_derived_cl353,plain,
( ~ ( in @ '#sk3' @ ( powerset @ '#sk1' ) )
| ~ ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
| ~ ( in @ ( setminus @ '#sk1' @ ( binunion @ '#sk2' @ '#sk3' ) ) @ ( powerset @ '#sk1' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl41,zip_derived_cl351]) ).
thf(zip_derived_cl40,plain,
in @ '#sk3' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl33,plain,
in @ '#sk2' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl354,plain,
~ ( in @ ( setminus @ '#sk1' @ ( binunion @ '#sk2' @ '#sk3' ) ) @ ( powerset @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl353,zip_derived_cl40,zip_derived_cl33]) ).
thf(zip_derived_cl25_001,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( powerset @ X2 ) )
| ( in @ ( setminus @ X2 @ X4 ) @ ( powerset @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl356,plain,
~ ( in @ ( binunion @ '#sk2' @ '#sk3' ) @ ( powerset @ '#sk1' ) ),
inference('sup+',[status(thm)],[zip_derived_cl354,zip_derived_cl25]) ).
thf(zip_derived_cl359,plain,
( ~ ( in @ '#sk2' @ ( powerset @ '#sk1' ) )
| ~ ( in @ '#sk3' @ ( powerset @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl356]) ).
thf(zip_derived_cl33_002,plain,
in @ '#sk2' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl40_003,plain,
in @ '#sk3' @ ( powerset @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl360,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl359,zip_derived_cl33,zip_derived_cl40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.10 % Problem : SEU749^2 : TPTP v9.2.0. Released v3.7.0.
% 0.01/0.11 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OmG8mY3pzq true
% 0.11/0.31 % Computer : n031.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Oct 1 16:10:08 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.32 % Running in HO mode
% 0.51/0.62 % Total configuration time : 828
% 0.51/0.62 % Estimated wc time : 1656
% 0.51/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.69 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.60/0.69 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.60/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.60/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.70 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.73/0.70 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 17.02/2.70 % Solved by lams/40_b.comb.sh.
% 17.02/2.70 % done 130 iterations in 1.958s
% 17.02/2.70 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 17.02/2.70 % SZS output start Refutation
% See solution above
% 17.02/2.70
% 17.02/2.70
% 17.02/2.70 % Terminating...
% 17.17/2.84 % Runner terminated.
% 17.17/2.85 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------