%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU773^2 : 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.MI1TDkp9yO true
% Computer : n024.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 04:56:17 PM UTC 2025
% Result : Theorem 0.57s 1.46s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 357 ( 8 equ; 0 cnn)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 1415 ( 72 ~; 66 |; 0 &;1064 @)
% ( 0 <=>; 150 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-4 aty)
% ( 63 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 189 ( 78 ^; 111 !; 0 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subbreln_type,type,
subbreln: $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk4_type',type,
'#sk4': $i > $i > $i > $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i > $i > $i > $i > $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(breln1,axiom,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ 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('2',plain,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln1,'1']) ).
thf('3',plain,
( breln1
= ( ^ [V_1: $i,V_2: $i] : ( breln @ V_1 @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(subbreln,axiom,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ) ).
thf('4',plain,
( subbreln
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( breln @ X4 @ X6 @ X8 )
=> ! [X10: $i] :
( ( breln @ X4 @ X6 @ X10 )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( subset @ X8 @ X10 ) ) ) ) ) ),
define([status(thm)]) ).
thf(subbreln1,conjecture,
( subbreln
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X4 @ X6 ) )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( subset @ X8 @ X10 ) ) ) )
=> ! [X16: $i,X18: $i] :
( ( subset @ X18 @ ( cartprod @ X16 @ X16 ) )
=> ! [X20: $i] :
( ( subset @ X20 @ ( cartprod @ X16 @ X16 ) )
=> ( ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ! [X24: $i] :
( ( in @ X24 @ X16 )
=> ( ( in @ ( kpair @ X22 @ X24 ) @ X18 )
=> ( in @ ( kpair @ X22 @ X24 ) @ X20 ) ) ) )
=> ( subset @ X18 @ X20 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i,X8: $i] :
( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
=> ! [X10: $i] :
( ( subset @ X10 @ ( cartprod @ X4 @ X6 ) )
=> ( ! [X12: $i] :
( ( in @ X12 @ X4 )
=> ! [X14: $i] :
( ( in @ X14 @ X6 )
=> ( ( in @ ( kpair @ X12 @ X14 ) @ X8 )
=> ( in @ ( kpair @ X12 @ X14 ) @ X10 ) ) ) )
=> ( subset @ X8 @ X10 ) ) ) )
=> ! [X16: $i,X18: $i] :
( ( subset @ X18 @ ( cartprod @ X16 @ X16 ) )
=> ! [X20: $i] :
( ( subset @ X20 @ ( cartprod @ X16 @ X16 ) )
=> ( ! [X22: $i] :
( ( in @ X22 @ X16 )
=> ! [X24: $i] :
( ( in @ X24 @ X16 )
=> ( ( in @ ( kpair @ X22 @ X24 ) @ X18 )
=> ( in @ ( kpair @ X22 @ X24 ) @ X20 ) ) ) )
=> ( subset @ X18 @ X20 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ Y0 @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( !!
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ '#sk1' )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl6,plain,
~ ( ( subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ '#sk2' )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ '#sk2' @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ '#sk1' )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ '#sk2' )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ '#sk2' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl11,plain,
~ ( ( subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk1' ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk2' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) )
=> ( subset @ '#sk2' @ '#sk3' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl13,plain,
subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
=> ( !!
@ ^ [Y3: $i] :
( ( subset @ Y3 @ ( cartprod @ Y0 @ Y1 ) )
=> ( ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( !!
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
=> ( ( in @ ( kpair @ Y4 @ Y5 ) @ Y2 )
=> ( in @ ( kpair @ Y4 @ Y5 ) @ Y3 ) ) ) ) ) )
=> ( subset @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X2 @ Y0 ) )
=> ( !!
@ ^ [Y2: $i] :
( ( subset @ Y2 @ ( cartprod @ X2 @ Y0 ) )
=> ( ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
=> ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y1 )
=> ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( subset @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( subset @ Y1 @ ( cartprod @ X2 @ X4 ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ X4 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y0 )
=> ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( subset @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
=> ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X6 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X6 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( subset @ Y0 @ ( cartprod @ X2 @ X4 ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ X4 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ X6 )
=> ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 ) ) ) ) ) )
=> ( subset @ X6 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X8 ) ) ) ) ) )
=> ( subset @ X6 @ X8 ) ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X8 ) ) ) ) ) )
=> ( subset @ X6 @ X8 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ X4 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X6 )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ X8 ) ) ) ) ) )
| ( subset @ X6 @ X8 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl20,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ Y0 ) @ X6 )
=> ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ Y0 ) @ X8 ) ) ) ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( subset @ X6 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ X4 )
=> ( ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ Y0 ) @ X6 )
=> ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ Y0 ) @ X8 ) ) ) )
| ( subset @ X6 @ X8 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) @ X4 )
=> ( ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
=> ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X8 ) ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( subset @ X6 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
=> ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X8 ) )
| ( subset @ X6 @ X8 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X8 )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( subset @ X6 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( kpair @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) ) @ X6 )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ( subset @ X6 @ X8 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl14,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk2' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) )
=> ( subset @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl16,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ '#sk1' )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk2' )
=> ( in @ ( kpair @ Y0 @ Y1 ) @ '#sk3' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( in @ X2 @ '#sk1' )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( in @ ( kpair @ X2 @ Y0 ) @ '#sk2' )
=> ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] :
( ~ ( in @ X2 @ '#sk1' )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk1' )
=> ( ( in @ ( kpair @ X2 @ Y0 ) @ '#sk2' )
=> ( in @ ( kpair @ X2 @ Y0 ) @ '#sk3' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ '#sk1' )
=> ( ( in @ ( kpair @ X2 @ X4 ) @ '#sk2' )
=> ( in @ ( kpair @ X2 @ X4 ) @ '#sk3' ) ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ '#sk1' )
| ( ( in @ ( kpair @ X2 @ X4 ) @ '#sk2' )
=> ( in @ ( kpair @ X2 @ X4 ) @ '#sk3' ) )
| ~ ( in @ X2 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ ( kpair @ X2 @ X4 ) @ '#sk2' )
| ( in @ ( kpair @ X2 @ X4 ) @ '#sk3' )
| ~ ( in @ X2 @ '#sk1' )
| ~ ( in @ X4 @ '#sk1' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( subset @ '#sk2' @ X0 )
| ~ ( subset @ '#sk2' @ ( cartprod @ X2 @ X1 ) )
| ~ ( subset @ X0 @ ( cartprod @ X2 @ X1 ) )
| ~ ( in @ ( '#sk5' @ X2 @ X1 @ '#sk2' @ X0 ) @ '#sk1' )
| ~ ( in @ ( '#sk4' @ X2 @ X1 @ '#sk2' @ X0 ) @ '#sk1' )
| ( in @ ( kpair @ ( '#sk4' @ X2 @ X1 @ '#sk2' @ X0 ) @ ( '#sk5' @ X2 @ X1 @ '#sk2' @ X0 ) ) @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl29]) ).
thf(zip_derived_cl109,plain,
! [X0: $i,X1: $i] :
( ( subset @ '#sk2' @ '#sk3' )
| ~ ( subset @ '#sk2' @ ( cartprod @ X1 @ X0 ) )
| ~ ( subset @ '#sk3' @ ( cartprod @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ ( '#sk5' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( subset @ '#sk3' @ ( cartprod @ X1 @ X0 ) )
| ~ ( subset @ '#sk2' @ ( cartprod @ X1 @ X0 ) )
| ( subset @ '#sk2' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl31,zip_derived_cl64]) ).
thf(zip_derived_cl17,plain,
~ ( subset @ '#sk2' @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl17_001,plain,
~ ( subset @ '#sk2' @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl112,plain,
! [X0: $i,X1: $i] :
( ~ ( subset @ '#sk2' @ ( cartprod @ X1 @ X0 ) )
| ~ ( subset @ '#sk3' @ ( cartprod @ X1 @ X0 ) )
| ~ ( in @ ( '#sk4' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ ( '#sk5' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( subset @ '#sk3' @ ( cartprod @ X1 @ X0 ) )
| ~ ( subset @ '#sk2' @ ( cartprod @ X1 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl109,zip_derived_cl17,zip_derived_cl17]) ).
thf(zip_derived_cl113,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ ( '#sk5' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ ( '#sk4' @ X1 @ X0 @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( subset @ '#sk3' @ ( cartprod @ X1 @ X0 ) )
| ~ ( subset @ '#sk2' @ ( cartprod @ X1 @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl120,plain,
( ~ ( subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ) )
| ~ ( in @ ( '#sk4' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ~ ( in @ ( '#sk5' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl113]) ).
thf(zip_derived_cl8,plain,
subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13_002,plain,
subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl8_003,plain,
subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( '#sk4' @ X2 @ X4 @ X6 @ X8 ) @ X2 )
| ( subset @ X6 @ X8 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl33,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
| ( subset @ '#sk2' @ X0 )
| ( in @ ( '#sk4' @ '#sk1' @ '#sk1' @ '#sk2' @ X0 ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl22]) ).
thf(zip_derived_cl54,plain,
( ( in @ ( '#sk4' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ( subset @ '#sk2' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl33]) ).
thf(zip_derived_cl17_004,plain,
~ ( subset @ '#sk2' @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl60,plain,
in @ ( '#sk4' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl17]) ).
thf(zip_derived_cl13_005,plain,
subset @ '#sk3' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl8_006,plain,
subset @ '#sk2' @ ( cartprod @ '#sk1' @ '#sk1' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( in @ ( '#sk5' @ X2 @ X4 @ X6 @ X8 ) @ X4 )
| ( subset @ X6 @ X8 )
| ~ ( subset @ X6 @ ( cartprod @ X2 @ X4 ) )
| ~ ( subset @ X8 @ ( cartprod @ X2 @ X4 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl47,plain,
! [X0: $i] :
( ~ ( subset @ X0 @ ( cartprod @ '#sk1' @ '#sk1' ) )
| ( subset @ '#sk2' @ X0 )
| ( in @ ( '#sk5' @ '#sk1' @ '#sk1' @ '#sk2' @ X0 ) @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl27]) ).
thf(zip_derived_cl76,plain,
( ( in @ ( '#sk5' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1' )
| ( subset @ '#sk2' @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl47]) ).
thf(zip_derived_cl17_007,plain,
~ ( subset @ '#sk2' @ '#sk3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl82,plain,
in @ ( '#sk5' @ '#sk1' @ '#sk1' @ '#sk2' @ '#sk3' ) @ '#sk1',
inference(demod,[status(thm)],[zip_derived_cl76,zip_derived_cl17]) ).
thf(zip_derived_cl122,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl8,zip_derived_cl60,zip_derived_cl82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.32 % Problem : SEU773^2 : TPTP v9.2.0. Released v3.7.0.
% 0.12/0.33 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.MI1TDkp9yO true
% 0.13/0.54 % Computer : n024.cluster.edu
% 0.13/0.54 % Model : x86_64 x86_64
% 0.13/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.54 % Memory : 8042.1875MB
% 0.13/0.54 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.54 % CPULimit : 300
% 0.13/0.54 % WCLimit : 300
% 0.13/0.54 % DateTime : Wed Oct 1 16:12:53 EDT 2025
% 0.13/0.55 % CPUTime :
% 0.13/0.55 % Running portfolio for 300 s
% 0.13/0.56 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.58 % Number of cores: 8
% 0.18/0.58 % Python version: Python 3.6.8
% 0.19/0.59 % Running in HO mode
% 0.51/1.13 % Total configuration time : 828
% 0.51/1.13 % Estimated wc time : 1656
% 0.51/1.13 % Estimated cpu time (8 cpus) : 207.0
% 0.55/1.30 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/1.32 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/1.35 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/1.36 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/1.36 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.57/1.38 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.57/1.40 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/1.45 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/1.46 % Solved by lams/35_full_unif4.sh.
% 0.57/1.46 % done 61 iterations in 0.085s
% 0.57/1.46 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.57/1.46 % SZS output start Refutation
% See solution above
% 0.57/1.46
% 0.57/1.46
% 0.57/1.46 % Terminating...
% 2.00/1.70 % Runner terminated.
% 2.04/1.73 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------