%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU620^2 : 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.rtudC4DJUm true
% Computer : n011.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 04:55:24 PM UTC 2025
% Result : Theorem 0.41s 0.87s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 44 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1063 ( 22 ~; 8 |; 42 &; 956 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 7 con; 0-2 aty)
% ( 10 !!; 21 ??; 0 @@+; 0 @@-)
% Number of variables : 112 ( 40 ^; 58 !; 14 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf('#sk2_type',type,
'#sk2': $i ).
thf(iskpair_type,type,
iskpair: $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(kpairiskpair_type,type,
kpairiskpair: $o ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf('#sk3_type',type,
'#sk3': $i > $i > $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i ).
thf(kpairiskpair,axiom,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
thf('0',plain,
( kpairiskpair
= ( ! [X4: $i,X6: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) ) ),
define([status(thm)]) ).
thf(iskpair,axiom,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ? [Xy: $i] :
( ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
& ( in @ Xy @ ( setunion @ A ) ) )
& ( in @ Xx @ ( setunion @ A ) ) ) ) ) ).
thf('1',plain,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ? [Xy: $i] :
( ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
& ( in @ Xy @ ( setunion @ A ) ) )
& ( in @ Xx @ ( setunion @ A ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iskpair]) ).
thf('2',plain,
( iskpair
= ( ^ [V_1: $i] :
? [X4: $i] :
( ? [X6: $i] :
( ( V_1
= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) )
& ( in @ X6 @ ( setunion @ V_1 ) ) )
& ( in @ X4 @ ( setunion @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(kpairp,conjecture,
( kpairiskpair
=> ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i] :
? [X8: $i] :
( ( in @ X8 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X10: $i] :
( ( in @ X10 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [X12: $i,X14: $i] :
? [X16: $i] :
( ( in @ X16 @ ( setunion @ ( kpair @ X12 @ X14 ) ) )
& ? [X18: $i] :
( ( in @ X18 @ ( setunion @ ( kpair @ X12 @ X14 ) ) )
& ( ( kpair @ X12 @ X14 )
= ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i] :
? [X8: $i] :
( ( in @ X8 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )
& ? [X10: $i] :
( ( in @ X10 @ ( setunion @ ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X6 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ! [X12: $i,X14: $i] :
? [X16: $i] :
( ( in @ X16 @ ( setunion @ ( kpair @ X12 @ X14 ) ) )
& ? [X18: $i] :
( ( in @ X18 @ ( setunion @ ( kpair @ X12 @ X14 ) ) )
& ( ( kpair @ X12 @ X14 )
= ( setadjoin @ ( setadjoin @ X16 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X16 @ ( setadjoin @ X18 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( kpair @ Y0 @ Y1 ) ) )
& ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ ( kpair @ Y0 @ Y1 ) ) )
& ( ( kpair @ Y0 @ Y1 )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl16,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i] :
( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk3' @ X2 @ X4 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(kpair,axiom,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(zip_derived_cl0,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf,[status(esa)],[kpair]) ).
thf(zip_derived_cl3,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1
@ X2 ) ),
inference(ho_complete_eq,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk3' @ X2 @ X4 ) @ ( setunion @ ( kpair @ X2 @ X4 ) ) )
& ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl20,zip_derived_cl5]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] : ( in @ ( '#sk3' @ X2 @ X4 ) @ ( setunion @ ( kpair @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( '#sk3' @ X2 @ X4 ) @ ( setadjoin @ ( '#sk4' @ X2 @ X4 ) @ emptyset ) ) @ emptyset ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl5_001,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5_002,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5_003,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 ) @ ( setunion @ ( kpair @ X2 @ X4 ) ) )
& ( ( kpair @ X2 @ X4 )
= ( kpair @ ( '#sk3' @ X2 @ X4 ) @ ( '#sk4' @ X2 @ X4 ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26,zip_derived_cl5,zip_derived_cl5,zip_derived_cl5]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] : ( in @ ( '#sk4' @ X2 @ X4 ) @ ( setunion @ ( kpair @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl15,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( kpair @ Y0 @ Y1 ) ) )
& ( ??
@ ^ [Y3: $i] :
( ( in @ Y3 @ ( setunion @ ( kpair @ Y0 @ Y1 ) ) )
& ( ( kpair @ Y0 @ Y1 )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y3 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl17,plain,
~ ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( kpair @ '#sk1' @ Y0 ) ) )
& ( ??
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setunion @ ( kpair @ '#sk1' @ Y0 ) ) )
& ( ( kpair @ '#sk1' @ Y0 )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl19,plain,
~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ??
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ( kpair @ '#sk1' @ '#sk2' )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] :
~ ( ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ( kpair @ '#sk1' @ '#sk2' )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ~ ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
| ~ ( ??
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ( kpair @ '#sk1' @ '#sk2' )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ X4 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ( kpair @ '#sk1' @ '#sk2' )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X4 @ emptyset ) ) @ emptyset ) ) ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl5_004,plain,
! [X1: $i,X2: $i] :
( ( kpair @ X1 @ X2 )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ X4 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
& ( ( kpair @ '#sk1' @ '#sk2' )
= ( kpair @ X2 @ X4 ) ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl27,zip_derived_cl5]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
| ( ( kpair @ '#sk1' @ '#sk2' )
!= ( kpair @ X2 @ X4 ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
| ( ( kpair @ '#sk1' @ '#sk2' )
!= ( kpair @ X2 @ X4 ) )
| ~ ( in @ X2 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl46,plain,
! [X0: $i] :
( ~ ( in @ X0 @ ( setunion @ ( kpair @ '#sk1' @ '#sk2' ) ) )
| ( ( kpair @ '#sk1' @ '#sk2' )
!= ( kpair @ X0 @ ( '#sk4' @ '#sk1' @ '#sk2' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl29,zip_derived_cl34]) ).
thf(zip_derived_cl70,plain,
( ( kpair @ '#sk1' @ '#sk2' )
!= ( kpair @ ( '#sk3' @ '#sk1' @ '#sk2' ) @ ( '#sk4' @ '#sk1' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl23,zip_derived_cl46]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ( kpair @ X2 @ X4 )
= ( kpair @ ( '#sk3' @ X2 @ X4 ) @ ( '#sk4' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl33,plain,
! [X2: $i,X4: $i] :
( ( kpair @ X2 @ X4 )
= ( kpair @ ( '#sk3' @ X2 @ X4 ) @ ( '#sk4' @ X2 @ X4 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl79,plain,
( ( kpair @ '#sk1' @ '#sk2' )
!= ( kpair @ '#sk1' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl70,zip_derived_cl33]) ).
thf(zip_derived_cl80,plain,
$false,
inference(simplify,[status(thm)],[zip_derived_cl79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.09 % Problem : SEU620^2 : TPTP v9.2.0. Released v3.7.0.
% 0.06/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rtudC4DJUm true
% 0.07/0.29 % Computer : n011.cluster.edu
% 0.07/0.29 % Model : x86_64 x86_64
% 0.07/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.29 % Memory : 8042.1875MB
% 0.07/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.29 % CPULimit : 300
% 0.07/0.29 % WCLimit : 300
% 0.07/0.29 % DateTime : Wed Oct 1 16:05:38 EDT 2025
% 0.07/0.29 % CPUTime :
% 0.07/0.29 % Running portfolio for 300 s
% 0.07/0.29 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.29 % Number of cores: 8
% 0.07/0.29 % Python version: Python 3.6.8
% 0.07/0.30 % Running in HO mode
% 0.37/0.59 % Total configuration time : 828
% 0.37/0.59 % Estimated wc time : 1656
% 0.37/0.59 % Estimated cpu time (8 cpus) : 207.0
% 0.40/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.40/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.40/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.40/0.83 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.41/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.41/0.87 % Solved by lams/35_full_unif4.sh.
% 0.41/0.87 % done 24 iterations in 0.048s
% 0.41/0.87 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.41/0.87 % SZS output start Refutation
% See solution above
% 0.41/0.87
% 0.41/0.87
% 0.41/0.87 % Terminating...
% 1.77/1.17 % Runner terminated.
% 1.77/1.19 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------