%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU707^2 : 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.NP6j5eSFnE true
% Computer : n007.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 04:55:52 PM UTC 2025
% Result : Theorem 0.62s 0.94s
% Output : Refutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 414 ( 133 equ; 24 cnn)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 910 ( 74 ~; 57 |; 74 &; 501 @)
% ( 0 <=>; 129 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 12 usr; 11 con; 0-4 aty)
% ( 75 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 238 ( 140 ^; 98 !; 0 ?; 238 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk3_type',type,
'#sk3': $i ).
thf(iftrueProp1_type,type,
iftrueProp1: $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(if_type,type,
if: $i > $o > $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf('#sk2_type',type,
'#sk2': $o ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(theeq_type,type,
theeq: $o ).
thf(ifSingleton_type,type,
ifSingleton: $o ).
thf(setunion_type,type,
setunion: $i > $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(theeq,axiom,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ) ).
thf('0',plain,
( theeq
= ( ! [X4: $i] :
( ( singleton @ X4 )
=> ! [X6: $i] :
( ( in @ X6 @ X4 )
=> ( ( setunion @ X4 )
= X6 ) ) ) ) ),
define([status(thm)]) ).
thf(if,axiom,
( if
= ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
( setunion
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ).
thf('1',plain,
( if
= ( ^ [A: $i,Xphi: $o,Xx: $i,Xy: $i] :
( setunion
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[if]) ).
thf('2',plain,
( if
= ( ^ [V_1: $i,V_2: $o,V_3: $i,V_4: $i] :
( setunion
@ ( dsetconstr @ V_1
@ ^ [V_5: $i] :
( ( V_2
& ( V_5 = V_3 ) )
| ( ~ V_2
& ( V_5 = V_4 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(ifSingleton,axiom,
( ifSingleton
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
thf('3',plain,
( ifSingleton
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( singleton
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(iftrueProp1,axiom,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
thf('4',plain,
( iftrueProp1
= ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( X6
& ( V_1 = X8 ) )
| ( ~ X6
& ( V_1 = X10 ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(iftrue,conjecture,
( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( ( V_1 = X10 )
& ~ X6 )
| ( ( V_1 = X8 )
& X6 ) ) ) ) ) ) )
=> ( ! [X12: $i,X14: $o,X16: $i] :
( ( in @ X16 @ X12 )
=> ! [X18: $i] :
( ( in @ X18 @ X12 )
=> ( singleton
@ ( dsetconstr @ X12
@ ^ [V_2: $i] :
( ( ( V_2 = X18 )
& ~ X14 )
| ( ( V_2 = X16 )
& X14 ) ) ) ) ) )
=> ( ! [X20: $i] :
( ( singleton @ X20 )
=> ! [X22: $i] :
( ( in @ X22 @ X20 )
=> ( ( setunion @ X20 )
= X22 ) ) )
=> ! [X24: $i,X26: $o,X28: $i] :
( ( in @ X28 @ X24 )
=> ! [X30: $i] :
( ( in @ X30 @ X24 )
=> ( X26
=> ( ( setunion
@ ( dsetconstr @ X24
@ ^ [V_3: $i] :
( ( ( V_3 = X30 )
& ~ X26 )
| ( ( V_3 = X28 )
& X26 ) ) ) )
= X28 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( X6
=> ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] :
( ( ( V_1 = X10 )
& ~ X6 )
| ( ( V_1 = X8 )
& X6 ) ) ) ) ) ) )
=> ( ! [X12: $i,X14: $o,X16: $i] :
( ( in @ X16 @ X12 )
=> ! [X18: $i] :
( ( in @ X18 @ X12 )
=> ( singleton
@ ( dsetconstr @ X12
@ ^ [V_2: $i] :
( ( ( V_2 = X18 )
& ~ X14 )
| ( ( V_2 = X16 )
& X14 ) ) ) ) ) )
=> ( ! [X20: $i] :
( ( singleton @ X20 )
=> ! [X22: $i] :
( ( in @ X22 @ X20 )
=> ( ( setunion @ X20 )
= X22 ) ) )
=> ! [X24: $i,X26: $o,X28: $i] :
( ( in @ X28 @ X24 )
=> ! [X30: $i] :
( ( in @ X30 @ X24 )
=> ( X26
=> ( ( setunion
@ ( dsetconstr @ X24
@ ^ [V_3: $i] :
( ( ( V_3 = X30 )
& ~ X26 )
| ( ( V_3 = X28 )
& X26 ) ) ) )
= X28 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( setunion @ Y0 )
= Y1 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) )
= Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( Y0
=> ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y3: $i] :
( ( ( Y3 = Y2 )
& ( (~) @ Y0 ) )
| ( ( Y3 = Y1 )
& Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( X4
=> ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ X4 ) )
| ( ( Y2 = Y0 )
& X4 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl9,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
=> ( $true
=> ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ $true ) )
| ( ( Y2 = Y0 )
& $true ) ) ) ) ) ) ) ) ),
inference('ho.refine.early.bird',[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl68,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
=> ( in @ Y0
@ ( dsetconstr @ X0
@ ^ [Y2: $i] : ( Y2 = Y0 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl69,plain,
! [X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : ( Y1 = X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl70,plain,
! [X0: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : ( Y1 = X2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl71,plain,
! [X0: $i,X2: $i,X4: $i] :
( ( ( in @ X4 @ X0 )
=> ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X2 ) ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl72,plain,
! [X0: $i,X2: $i,X4: $i] :
( ~ ( in @ X4 @ X0 )
| ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X2 ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl73,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( in @ X1
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X1 ) ) ) ),
inference(condensation,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( setunion @ Y0 )
= Y1 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) )
= Y2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( setunion @ Y0 )
= Y1 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) )
= Y2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: $i] :
( ( singleton @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( setunion @ Y0 )
= Y1 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( ( singleton @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( setunion @ X2 )
= Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl22,plain,
! [X2: $i] :
( ~ ( singleton @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( setunion @ X2 )
= Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ X2 )
=> ( ( setunion @ X2 )
= X4 ) )
| ~ ( singleton @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ X2 )
| ( ( setunion @ X2 )
= X4 )
| ~ ( singleton @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ X2 )
| ( ( setunion @ X2 )
= X4 )
| ~ ( singleton @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl92,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ X1 )
| ~ ( singleton
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( Y0 = X0 ) ) )
| ( ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( Y0 = X0 ) ) )
= X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl35]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( singleton
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl10,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [Y3: $i] :
( ( ( Y3 = Y2 )
& ( (~) @ Y0 ) )
| ( ( Y3 = Y1 )
& Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( singleton
@ ( dsetconstr @ X2
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ X4 ) )
| ( ( Y2 = Y0 )
& X4 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ $false ) )
| ( ( Y2 = Y0 )
& $false ) ) ) ) ) ) ) ),
inference('ho.refine.early.bird',[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl44,plain,
! [X0: $i] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [Y2: $i] : ( Y2 = Y1 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl45,plain,
! [X0: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : ( Y1 = Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl46,plain,
! [X0: $i,X2: $i] :
( ~ ( in @ X2 @ X0 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [Y1: $i] : ( Y1 = Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl47,plain,
! [X0: $i,X2: $i,X4: $i] :
( ( ( in @ X4 @ X0 )
=> ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X4 ) ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl48,plain,
! [X0: $i,X2: $i,X4: $i] :
( ~ ( in @ X4 @ X0 )
| ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X4 ) ) )
| ~ ( in @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X1 @ X0 )
| ( singleton
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( Y0 = X1 ) ) ) ),
inference(condensation,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl107,plain,
! [X0: $i,X1: $i] :
( ( ( setunion
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( Y0 = X0 ) ) )
= X0 )
| ~ ( in @ X0 @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl92,zip_derived_cl49]) ).
thf(zip_derived_cl12,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( Y1
=> ( ( setunion
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] :
( ( ( Y4 = Y3 )
& ( (~) @ Y1 ) )
| ( ( Y4 = Y2 )
& Y1 ) ) ) )
= Y2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl19,plain,
~ ( !!
@ ^ [Y0: $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( Y0
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y3: $i] :
( ( ( Y3 = Y2 )
& ( (~) @ Y0 ) )
| ( ( Y3 = Y1 )
& Y0 ) ) ) )
= Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl23,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( '#sk2'
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y2: $i] :
( ( ( Y2 = Y1 )
& ( (~) @ '#sk2' ) )
| ( ( Y2 = Y0 )
& '#sk2' ) ) ) )
= Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl27,plain,
~ ( ( in @ '#sk3' @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( '#sk2'
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ '#sk2' ) )
| ( ( Y1 = '#sk3' )
& '#sk2' ) ) ) )
= '#sk3' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( '#sk2'
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& ( (~) @ '#sk2' ) )
| ( ( Y1 = '#sk3' )
& '#sk2' ) ) ) )
= '#sk3' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl36,plain,
~ ( ( in @ '#sk4' @ '#sk1' )
=> ( '#sk2'
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk4' )
& ( (~) @ '#sk2' ) )
| ( ( Y0 = '#sk3' )
& '#sk2' ) ) ) )
= '#sk3' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl38,plain,
~ ( '#sk2'
=> ( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk4' )
& ( (~) @ '#sk2' ) )
| ( ( Y0 = '#sk3' )
& '#sk2' ) ) ) )
= '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl40,plain,
( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk4' )
& ( (~) @ '#sk2' ) )
| ( ( Y0 = '#sk3' )
& '#sk2' ) ) ) )
!= '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl41,plain,
( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk4' )
& ( (~) @ '#sk2' ) )
| ( ( Y0 = '#sk3' )
& '#sk2' ) ) ) )
!= '#sk3' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl39,plain,
'#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl39_001,plain,
'#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl42,plain,
( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] :
( ( ( Y0 = '#sk4' )
& ( (~) @ $true ) )
| ( ( Y0 = '#sk3' )
& $true ) ) ) )
!= '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl41,zip_derived_cl39,zip_derived_cl39]) ).
thf(zip_derived_cl43,plain,
( ( setunion
@ ( dsetconstr @ '#sk1'
@ ^ [Y0: $i] : ( Y0 = '#sk3' ) ) )
!= '#sk3' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl109,plain,
( ( '#sk3' != '#sk3' )
| ~ ( in @ '#sk3' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl43]) ).
thf(zip_derived_cl31,plain,
in @ '#sk3' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl116,plain,
'#sk3' != '#sk3',
inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl31]) ).
thf(zip_derived_cl117,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU707^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.NP6j5eSFnE true
% 0.15/0.34 % Computer : n007.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Wed Oct 1 16:09:53 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.35 % Number of cores: 8
% 0.15/0.35 % Python version: Python 3.6.8
% 0.15/0.35 % Running in HO mode
% 0.59/0.69 % Total configuration time : 828
% 0.59/0.69 % Estimated wc time : 1656
% 0.59/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.60/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.60/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.60/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.60/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.62/0.94 % Solved by lams/30_sp5.sh.
% 0.62/0.94 % done 25 iterations in 0.101s
% 0.62/0.94 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.62/0.94 % SZS output start Refutation
% See solution above
% 0.62/0.94
% 0.62/0.94
% 0.62/0.94 % Terminating...
% 1.88/1.02 % Runner terminated.
% 1.88/1.04 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------