%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU675^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.91EoD5nTY5 true
% Computer : n001.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 04:55:41 PM UTC 2025
% Result : Theorem 0.53s 0.91s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 345 ( 57 equ; 0 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1262 ( 37 ~; 18 |; 54 &;1038 @)
% ( 0 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 9 con; 0-3 aty)
% ( 42 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 242 ( 188 ^; 47 !; 7 ?; 242 :)
% Comments :
%------------------------------------------------------------------------------
thf(singleton_type,type,
singleton: $i > $o ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf('#sk9_type',type,
'#sk9': $i > $i > $i ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(dsetconstrER_type,type,
dsetconstrER: $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(funcSet,axiom,
( funcSet
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
@ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ) ).
thf(func,axiom,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
thf(breln,axiom,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf('0',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('1',plain,
( breln
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( subset @ V_3 @ ( cartprod @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(ex1,axiom,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
thf(singleton,axiom,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ) ).
thf('2',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('3',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'3']) ).
thf('5',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[func,'1','5','3']) ).
thf('7',plain,
( func
= ( ^ [V_1: $i,V_2: $i,V_3: $i] :
( ( breln @ V_1 @ V_2 @ V_3 )
& ! [X4: $i] :
( ( in @ X4 @ V_1 )
=> ( ex1 @ V_2
@ ^ [V_4: $i] : ( in @ ( kpair @ X4 @ V_4 ) @ V_3 ) ) ) ) ) ),
define([status(thm)]) ).
thf('8',plain,
( funcSet
= ( ^ [A: $i,B: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ A @ B ) )
@ ^ [Xf: $i] : ( func @ A @ B @ Xf ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[funcSet,'7','5','3']) ).
thf('9',plain,
( funcSet
= ( ^ [V_1: $i,V_2: $i] :
( dsetconstr @ ( powerset @ ( cartprod @ V_1 @ V_2 ) )
@ ^ [V_3: $i] : ( func @ V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(dsetconstrER,axiom,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ) ).
thf('10',plain,
( dsetconstrER
= ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(infuncsetfunc,conjecture,
( dsetconstrER
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ! [X10: $i,X12: $i,X14: $i] :
( ( in @ X14
@ ( dsetconstr @ ( powerset @ ( cartprod @ X10 @ X12 ) )
@ ^ [V_2: $i] :
( ! [X16: $i] :
( ( in @ X16 @ X10 )
=> ? [X18: $i] :
( ( in @ X18
@ ( dsetconstr @ X12
@ ^ [V_4: $i] : ( in @ ( kpair @ X16 @ V_4 ) @ V_2 ) ) )
& ( ( dsetconstr @ X12
@ ^ [V_3: $i] : ( in @ ( kpair @ X16 @ V_3 ) @ V_2 ) )
= ( setadjoin @ X18 @ emptyset ) ) ) )
& ( subset @ V_2 @ ( cartprod @ X10 @ X12 ) ) ) ) )
=> ( ! [X20: $i] :
( ( in @ X20 @ X10 )
=> ? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ X12
@ ^ [V_6: $i] : ( in @ ( kpair @ X20 @ V_6 ) @ X14 ) ) )
& ( ( dsetconstr @ X12
@ ^ [V_5: $i] : ( in @ ( kpair @ X20 @ V_5 ) @ X14 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) )
& ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8
@ ( dsetconstr @ X4
@ ^ [V_1: $i] : ( X6 @ V_1 ) ) )
=> ( X6 @ X8 ) )
=> ! [X10: $i,X12: $i,X14: $i] :
( ( in @ X14
@ ( dsetconstr @ ( powerset @ ( cartprod @ X10 @ X12 ) )
@ ^ [V_2: $i] :
( ! [X16: $i] :
( ( in @ X16 @ X10 )
=> ? [X18: $i] :
( ( in @ X18
@ ( dsetconstr @ X12
@ ^ [V_4: $i] : ( in @ ( kpair @ X16 @ V_4 ) @ V_2 ) ) )
& ( ( dsetconstr @ X12
@ ^ [V_3: $i] : ( in @ ( kpair @ X16 @ V_3 ) @ V_2 ) )
= ( setadjoin @ X18 @ emptyset ) ) ) )
& ( subset @ V_2 @ ( cartprod @ X10 @ X12 ) ) ) ) )
=> ( ! [X20: $i] :
( ( in @ X20 @ X10 )
=> ? [X22: $i] :
( ( in @ X22
@ ( dsetconstr @ X12
@ ^ [V_6: $i] : ( in @ ( kpair @ X20 @ V_6 ) @ X14 ) ) )
& ( ( dsetconstr @ X12
@ ^ [V_5: $i] : ( in @ ( kpair @ X20 @ V_5 ) @ X14 ) )
= ( setadjoin @ X22 @ emptyset ) ) ) )
& ( subset @ X14 @ ( cartprod @ X10 @ X12 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y3: $i] :
( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y3: $i] :
( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i > $o] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( dsetconstr @ X2 @ Y0 ) )
=> ( Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( dsetconstr @ X2 @ X4 ) )
=> ( X4 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
=> ( X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i > $o,X6: $i] :
( ~ ( in @ X6 @ ( dsetconstr @ X2 @ X4 ) )
| ( X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ ( powerset @ ( cartprod @ Y0 @ Y1 ) )
@ ^ [Y3: $i] :
( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ??
@ ^ [Y5: $i] :
( ( in @ Y5
@ ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y6: $i] : ( in @ ( kpair @ Y4 @ Y6 ) @ Y3 ) )
= ( setadjoin @ Y5 @ emptyset ) ) ) ) ) )
& ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y1
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ ( powerset @ ( cartprod @ '#sk1' @ Y0 ) )
@ ^ [Y2: $i] :
( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk1' )
=> ( ??
@ ^ [Y4: $i] :
( ( in @ Y4
@ ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y5: $i] : ( in @ ( kpair @ Y3 @ Y5 ) @ Y2 ) )
= ( setadjoin @ Y4 @ emptyset ) ) ) ) ) )
& ( subset @ Y2 @ ( cartprod @ '#sk1' @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ '#sk1' @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ ( powerset @ ( cartprod @ '#sk1' @ '#sk2' ) )
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ??
@ ^ [Y3: $i] :
( ( in @ Y3
@ ( dsetconstr @ '#sk2'
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) )
= ( setadjoin @ Y3 @ emptyset ) ) ) ) ) )
& ( subset @ Y1 @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl9,plain,
~ ( ( in @ '#sk5'
@ ( dsetconstr @ ( powerset @ ( cartprod @ '#sk1' @ '#sk2' ) )
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl11,plain,
( in @ '#sk5'
@ ( dsetconstr @ ( powerset @ ( cartprod @ '#sk1' @ '#sk2' ) )
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl72,plain,
( ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ??
@ ^ [Y2: $i] :
( ( in @ Y2
@ ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) )
= ( setadjoin @ Y2 @ emptyset ) ) ) ) ) )
& ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk2' ) ) )
@ '#sk5' ),
inference('sup+',[status(thm)],[zip_derived_cl10,zip_derived_cl11]) ).
thf(zip_derived_cl73,plain,
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl75,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl77,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl78,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ X2 @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl79,plain,
! [X2: $i] :
( ( ( in @ ( '#sk9' @ '#sk5' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk9' @ '#sk5' @ X2 ) @ emptyset ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk9' @ '#sk5' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl82,plain,
! [X2: $i] :
( ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ ( '#sk9' @ '#sk5' @ X2 ) @ emptyset ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ( in @ ( '#sk9' @ '#sk5' @ X2 )
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ X2 @ Y0 ) @ '#sk5' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl79]) ).
thf(zip_derived_cl12,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
& ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl13,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( in @ Y1
@ ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ '#sk5' ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
( ~ ( ( in @ '#sk8' @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl16,plain,
( ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0
@ ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y1: $i] : ( in @ ( kpair @ '#sk8' @ Y1 ) @ '#sk5' ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ~ ( ( in @ X2
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
& ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
= ( setadjoin @ X2 @ emptyset ) ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ X2 @ emptyset ) )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl76,plain,
subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl84,plain,
! [X2: $i] :
( ~ ( in @ X2
@ ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) ) )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ X2 @ emptyset ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19,zip_derived_cl76]) ).
thf(zip_derived_cl94,plain,
( ~ ( in @ '#sk8' @ '#sk1' )
| ( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl84]) ).
thf(zip_derived_cl15,plain,
( ( in @ '#sk8' @ '#sk1' )
| ~ ( subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl76_001,plain,
subset @ '#sk5' @ ( cartprod @ '#sk1' @ '#sk2' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl83,plain,
in @ '#sk8' @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl15,zip_derived_cl76]) ).
thf(zip_derived_cl96,plain,
( ( dsetconstr @ '#sk2'
@ ^ [Y0: $i] : ( in @ ( kpair @ '#sk8' @ Y0 ) @ '#sk5' ) )
!= ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset ) ),
inference(demod,[status(thm)],[zip_derived_cl94,zip_derived_cl83]) ).
thf(zip_derived_cl97,plain,
( ( ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset )
!= ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset ) )
| ~ ( in @ '#sk8' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl96]) ).
thf(zip_derived_cl83_002,plain,
in @ '#sk8' @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl15,zip_derived_cl76]) ).
thf(zip_derived_cl98,plain,
( ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset )
!= ( setadjoin @ ( '#sk9' @ '#sk5' @ '#sk8' ) @ emptyset ) ),
inference(demod,[status(thm)],[zip_derived_cl97,zip_derived_cl83]) ).
thf(zip_derived_cl99,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU675^2 : TPTP v9.2.0. Released v3.7.0.
% 0.03/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.91EoD5nTY5 true
% 0.11/0.32 % Computer : n001.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Oct 1 16:03:53 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.51/0.64 % Total configuration time : 828
% 0.51/0.64 % Estimated wc time : 1656
% 0.51/0.64 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.53/0.76 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.53/0.91 % Solved by lams/20_acsne_simpl.sh.
% 0.53/0.91 % done 18 iterations in 0.111s
% 0.53/0.91 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.53/0.91 % SZS output start Refutation
% See solution above
% 0.53/0.91
% 0.53/0.91
% 0.53/0.91 % Terminating...
% 1.85/0.98 % Runner terminated.
% 1.85/1.00 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------