%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEU680^2 : 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.rdRk4JlIOo true
% Computer : n005.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 04:55:43 PM UTC 2025
% Result : Theorem 11.01s 2.01s
% Output : Refutation 11.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 60 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 35 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1342 ( 50 ~; 74 |; 14 &;1173 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 249 ( 79 ^; 163 !; 7 ?; 249 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(sk__11_type,type,
sk__11: $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk__9_type,type,
sk__9: $i > ( $i > $i ) > $i > $i > $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(func_type,type,
func: $i > $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(lamp_type,type,
lamp: $o ).
thf(lam_type,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(sk__13_type,type,
sk__13: $i > $i ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(sk__14_type,type,
sk__14: $i > $i > $i > $i ).
thf(dsetconstr_type,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(ex1_type,type,
ex1: $i > ( $i > $o ) > $o ).
thf(funcinfuncset_type,type,
funcinfuncset: $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(funcSet_type,type,
funcSet: $i > $i > $i ).
thf(sk__10_type,type,
sk__10: ( $i > $i ) > $i > $i > $i ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(sk__12_type,type,
sk__12: $i ).
thf(lamp,axiom,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
thf('0',plain,
( lamp
= ( ! [X4: $i,X6: $i,X8: $i > $i] :
( ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ( in @ ( X8 @ X10 ) @ X6 ) )
=> ( func @ X4 @ X6
@ ( lam @ X4 @ X6
@ ^ [V_1: $i] : ( X8 @ V_1 ) ) ) ) ) ),
define([status(thm)]) ).
thf(funcinfuncset,axiom,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
thf('1',plain,
( funcinfuncset
= ( ! [X4: $i,X6: $i,X8: $i] :
( ( func @ X4 @ X6 @ X8 )
=> ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) ) ) ),
define([status(thm)]) ).
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('2',plain,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[breln]) ).
thf('3',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('4',plain,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( A
= ( setadjoin @ Xx @ emptyset ) )
& ( in @ Xx @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[singleton]) ).
thf('5',plain,
( singleton
= ( ^ [V_1: $i] :
? [X4: $i] :
( ( V_1
= ( setadjoin @ X4 @ emptyset ) )
& ( in @ X4 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ex1,'5']) ).
thf('7',plain,
( ex1
= ( ^ [V_1: $i,V_2: $i > $o] :
( singleton
@ ( dsetconstr @ V_1
@ ^ [V_3: $i] : ( V_2 @ V_3 ) ) ) ) ),
define([status(thm)]) ).
thf('8',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,'3','7','5']) ).
thf('9',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(lam2p,conjecture,
( funcinfuncset
=> ( lamp
=> ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
( ! [X4: $i,X6: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
& ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ? [X12: $i] :
( ( ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
= ( setadjoin @ X12 @ emptyset ) )
& ( in @ X12
@ ( dsetconstr @ X6
@ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) ) )
=> ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) )
=> ( ! [X14: $i,X16: $i,X18: $i > $i] :
( ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ( in @ ( X18 @ X20 ) @ X16 ) )
=> ( ( subset
@ ( lam @ X14 @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) )
@ ( cartprod @ X14 @ X16 ) )
& ! [X22: $i] :
( ( in @ X22 @ X14 )
=> ? [X24: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_4: $i] :
( in @ ( kpair @ X22 @ V_4 )
@ ( lam @ X14 @ X16
@ ^ [V_5: $i] : ( X18 @ V_5 ) ) ) )
= ( setadjoin @ X24 @ emptyset ) )
& ( in @ X24
@ ( dsetconstr @ X16
@ ^ [V_6: $i] :
( in @ ( kpair @ X22 @ V_6 )
@ ( lam @ X14 @ X16
@ ^ [V_7: $i] : ( X18 @ V_7 ) ) ) ) ) ) ) ) )
=> ! [X26: $i,X28: $i,X30: $i > $i] :
( ! [X32: $i] :
( ( in @ X32 @ X26 )
=> ( in @ ( X30 @ X32 ) @ X28 ) )
=> ( in
@ ( lam @ X26 @ X28
@ ^ [V_8: $i] : ( X30 @ V_8 ) )
@ ( funcSet @ X26 @ X28 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: $i,X6: $i,X8: $i] :
( ( ( subset @ X8 @ ( cartprod @ X4 @ X6 ) )
& ! [X10: $i] :
( ( in @ X10 @ X4 )
=> ? [X12: $i] :
( ( ( dsetconstr @ X6
@ ^ [V_1: $i] : ( in @ ( kpair @ X10 @ V_1 ) @ X8 ) )
= ( setadjoin @ X12 @ emptyset ) )
& ( in @ X12
@ ( dsetconstr @ X6
@ ^ [V_2: $i] : ( in @ ( kpair @ X10 @ V_2 ) @ X8 ) ) ) ) ) )
=> ( in @ X8 @ ( funcSet @ X4 @ X6 ) ) )
=> ( ! [X14: $i,X16: $i,X18: $i > $i] :
( ! [X20: $i] :
( ( in @ X20 @ X14 )
=> ( in @ ( X18 @ X20 ) @ X16 ) )
=> ( ( subset
@ ( lam @ X14 @ X16
@ ^ [V_3: $i] : ( X18 @ V_3 ) )
@ ( cartprod @ X14 @ X16 ) )
& ! [X22: $i] :
( ( in @ X22 @ X14 )
=> ? [X24: $i] :
( ( ( dsetconstr @ X16
@ ^ [V_4: $i] :
( in @ ( kpair @ X22 @ V_4 )
@ ( lam @ X14 @ X16
@ ^ [V_5: $i] : ( X18 @ V_5 ) ) ) )
= ( setadjoin @ X24 @ emptyset ) )
& ( in @ X24
@ ( dsetconstr @ X16
@ ^ [V_6: $i] :
( in @ ( kpair @ X22 @ V_6 )
@ ( lam @ X14 @ X16
@ ^ [V_7: $i] : ( X18 @ V_7 ) ) ) ) ) ) ) ) )
=> ! [X26: $i,X28: $i,X30: $i > $i] :
( ! [X32: $i] :
( ( in @ X32 @ X26 )
=> ( in @ ( X30 @ X32 ) @ X28 ) )
=> ( in
@ ( lam @ X26 @ X28
@ ^ [V_8: $i] : ( X30 @ V_8 ) )
@ ( funcSet @ X26 @ X28 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl4,plain,
! [X4: $i] :
( ( in @ ( sk__13 @ X4 ) @ sk__12 )
| ~ ( in @ X4 @ sk__11 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset
@ ( lam @ X5 @ X6
@ ^ [Y0: $i] : ( X7 @ Y0 ) )
@ ( cartprod @ X5 @ X6 ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl12,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset @ ( lam @ X5 @ X6 @ X7 ) @ ( cartprod @ X5 @ X6 ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( in @ ( sk__9 @ X8 @ X7 @ X6 @ X5 )
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( in @ ( kpair @ X8 @ Y0 )
@ ( lam @ X5 @ X6
@ ^ [Y1: $i] : ( X7 @ Y1 ) ) ) ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl38,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( in @ ( sk__9 @ X8 @ X7 @ X6 @ X5 )
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ ( lam @ X5 @ X6 @ X7 ) ) ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl2,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
| ~ ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ X0 @ X2 @ X1 ) @ Y0 ) @ X0 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ X0 @ X2 @ X1 ) @ Y0 ) @ X0 ) )
!= ( setadjoin @ X3 @ emptyset ) )
| ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl40,plain,
! [X0: $i > $i,X1: $i,X2: $i,X3: $i] :
( ~ ( in @ ( X0 @ ( sk__10 @ X0 @ X1 @ X2 ) ) @ X1 )
| ~ ( in @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X3 ) @ X2 )
| ~ ( subset @ ( lam @ X2 @ X1 @ X0 ) @ ( cartprod @ X3 @ X1 ) )
| ( ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X3 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) )
!= ( setadjoin @ ( sk__9 @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X3 ) @ X0 @ X1 @ X2 ) @ emptyset ) )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X3 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl38,zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] :
( in @ ( kpair @ X8 @ Y0 )
@ ( lam @ X5 @ X6
@ ^ [Y1: $i] : ( X7 @ Y1 ) ) ) )
= ( setadjoin @ ( sk__9 @ X8 @ X7 @ X6 @ X5 ) @ emptyset ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl71,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ ( lam @ X5 @ X6 @ X7 ) ) )
= ( setadjoin @ ( sk__9 @ X8 @ X7 @ X6 @ X5 ) @ emptyset ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl219,plain,
! [X0: $i > $i,X1: $i,X2: $i,X3: $i] :
( ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X3 @ X1 ) )
| ~ ( subset @ ( lam @ X2 @ X1 @ X0 ) @ ( cartprod @ X3 @ X1 ) )
| ~ ( in @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X3 ) @ X2 )
| ~ ( in @ ( X0 @ ( sk__10 @ X0 @ X1 @ X2 ) ) @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl40,zip_derived_cl71]) ).
thf(zip_derived_cl232,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ~ ( in @ ( X2 @ ( sk__10 @ X2 @ X0 @ X1 ) ) @ X0 )
| ~ ( in @ ( X2 @ ( sk__10 @ X2 @ X0 @ X1 ) ) @ X0 )
| ~ ( in @ ( sk__14 @ ( lam @ X1 @ X0 @ X2 ) @ X0 @ X1 ) @ X1 )
| ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl219]) ).
thf(zip_derived_cl247,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) )
| ~ ( in @ ( sk__14 @ ( lam @ X1 @ X0 @ X2 ) @ X0 @ X1 ) @ X1 )
| ~ ( in @ ( X2 @ ( sk__10 @ X2 @ X0 @ X1 ) ) @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl232]) ).
thf(zip_derived_cl12_001,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset @ ( lam @ X5 @ X6 @ X7 ) @ ( cartprod @ X5 @ X6 ) )
| ~ ( in @ ( X7 @ ( sk__10 @ X7 @ X6 @ X5 ) ) @ X6 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl1,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl14,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ~ ( in @ ( X2 @ ( sk__10 @ X2 @ X0 @ X1 ) ) @ X0 )
| ( in @ ( sk__14 @ ( lam @ X1 @ X0 @ X2 ) @ X0 @ X1 ) @ X1 )
| ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl1]) ).
thf(zip_derived_cl256,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ~ ( in @ ( X2 @ ( sk__10 @ X2 @ X0 @ X1 ) ) @ X0 )
| ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl247,zip_derived_cl14]) ).
thf(zip_derived_cl3,plain,
~ ( in
@ ( lam @ sk__11 @ sk__12
@ ^ [Y0: $i] : ( sk__13 @ Y0 ) )
@ ( funcSet @ sk__11 @ sk__12 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl11,plain,
~ ( in @ ( lam @ sk__11 @ sk__12 @ sk__13 ) @ ( funcSet @ sk__11 @ sk__12 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl257,plain,
~ ( in @ ( sk__13 @ ( sk__10 @ sk__13 @ sk__12 @ sk__11 ) ) @ sk__12 ),
inference('sup-',[status(thm)],[zip_derived_cl256,zip_derived_cl11]) ).
thf(zip_derived_cl273,plain,
~ ( in @ ( sk__10 @ sk__13 @ sk__12 @ sk__11 ) @ sk__11 ),
inference('sup-',[status(thm)],[zip_derived_cl4,zip_derived_cl257]) ).
thf(zip_derived_cl6,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset
@ ( lam @ X5 @ X6
@ ^ [Y0: $i] : ( X7 @ Y0 ) )
@ ( cartprod @ X5 @ X6 ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl33,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset @ ( lam @ X5 @ X6 @ X7 ) @ ( cartprod @ X5 @ X6 ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl1_002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
| ( in @ ( sk__14 @ X0 @ X2 @ X1 ) @ X1 )
| ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl34,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ( in @ ( sk__10 @ X2 @ X0 @ X1 ) @ X1 )
| ( in @ ( sk__14 @ ( lam @ X1 @ X0 @ X2 ) @ X0 @ X1 ) @ X1 )
| ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl33,zip_derived_cl1]) ).
thf(zip_derived_cl10,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] :
( in @ ( kpair @ X8 @ Y0 )
@ ( lam @ X5 @ X6
@ ^ [Y1: $i] : ( X7 @ Y1 ) ) ) )
= ( setadjoin @ ( sk__9 @ X8 @ X7 @ X6 @ X5 ) @ emptyset ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl63,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ ( lam @ X5 @ X6 @ X7 ) ) )
= ( setadjoin @ ( sk__9 @ X8 @ X7 @ X6 @ X5 ) @ emptyset ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl64,plain,
! [X0: $i,X1: $i,X2: $i > $i,X3: $i,X4: $i > $i] :
( ( in @ ( lam @ X0 @ X1 @ X2 ) @ ( funcSet @ X0 @ X1 ) )
| ( in @ ( sk__10 @ X2 @ X1 @ X0 ) @ X0 )
| ( in @ ( sk__10 @ X4 @ X3 @ X0 ) @ X0 )
| ( ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X0 @ X1 @ X2 ) @ X1 @ X0 ) @ Y0 ) @ ( lam @ X0 @ X3 @ X4 ) ) )
= ( setadjoin @ ( sk__9 @ ( sk__14 @ ( lam @ X0 @ X1 @ X2 ) @ X1 @ X0 ) @ X4 @ X3 @ X0 ) @ emptyset ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl63]) ).
thf(zip_derived_cl34_003,plain,
! [X0: $i,X1: $i,X2: $i > $i] :
( ( in @ ( sk__10 @ X2 @ X0 @ X1 ) @ X1 )
| ( in @ ( sk__14 @ ( lam @ X1 @ X0 @ X2 ) @ X0 @ X1 ) @ X1 )
| ( in @ ( lam @ X1 @ X0 @ X2 ) @ ( funcSet @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl33,zip_derived_cl1]) ).
thf(zip_derived_cl8,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( in @ ( sk__9 @ X8 @ X7 @ X6 @ X5 )
@ ( dsetconstr @ X6
@ ^ [Y0: $i] :
( in @ ( kpair @ X8 @ Y0 )
@ ( lam @ X5 @ X6
@ ^ [Y1: $i] : ( X7 @ Y1 ) ) ) ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl54,plain,
! [X5: $i,X6: $i,X7: $i > $i,X8: $i] :
( ~ ( in @ X8 @ X5 )
| ( in @ ( sk__9 @ X8 @ X7 @ X6 @ X5 )
@ ( dsetconstr @ X6
@ ^ [Y0: $i] : ( in @ ( kpair @ X8 @ Y0 ) @ ( lam @ X5 @ X6 @ X7 ) ) ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl59,plain,
! [X0: $i,X1: $i,X2: $i > $i,X3: $i,X4: $i > $i] :
( ( in @ ( lam @ X0 @ X1 @ X2 ) @ ( funcSet @ X0 @ X1 ) )
| ( in @ ( sk__10 @ X2 @ X1 @ X0 ) @ X0 )
| ( in @ ( sk__10 @ X4 @ X3 @ X0 ) @ X0 )
| ( in @ ( sk__9 @ ( sk__14 @ ( lam @ X0 @ X1 @ X2 ) @ X1 @ X0 ) @ X4 @ X3 @ X0 )
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X0 @ X1 @ X2 ) @ X1 @ X0 ) @ Y0 ) @ ( lam @ X0 @ X3 @ X4 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl54]) ).
thf(zip_derived_cl2_004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
| ~ ( in @ X3
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ X0 @ X2 @ X1 ) @ Y0 ) @ X0 ) ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ X0 @ X2 @ X1 ) @ Y0 ) @ X0 ) )
!= ( setadjoin @ X3 @ emptyset ) )
| ~ ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl375,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ~ ( subset @ ( lam @ X2 @ X1 @ X0 ) @ ( cartprod @ X2 @ X1 ) )
| ( ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) )
!= ( setadjoin @ ( sk__9 @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ X0 @ X1 @ X2 ) @ emptyset ) )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl59,zip_derived_cl2]) ).
thf(zip_derived_cl382,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) )
!= ( setadjoin @ ( sk__9 @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ X0 @ X1 @ X2 ) @ emptyset ) )
| ~ ( subset @ ( lam @ X2 @ X1 @ X0 ) @ ( cartprod @ X2 @ X1 ) )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl375]) ).
thf(zip_derived_cl33_005,plain,
! [X5: $i,X6: $i,X7: $i > $i] :
( ( subset @ ( lam @ X5 @ X6 @ X7 ) @ ( cartprod @ X5 @ X6 ) )
| ( in @ ( sk__10 @ X7 @ X6 @ X5 ) @ X5 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl492,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ( ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) )
!= ( setadjoin @ ( sk__9 @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ X0 @ X1 @ X2 ) @ emptyset ) ) ),
inference(clc,[status(thm)],[zip_derived_cl382,zip_derived_cl33]) ).
thf(zip_derived_cl494,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) )
!= ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sk__14 @ ( lam @ X2 @ X1 @ X0 ) @ X1 @ X2 ) @ Y0 ) @ ( lam @ X2 @ X1 @ X0 ) ) ) )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 ) ),
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl492]) ).
thf(zip_derived_cl504,plain,
! [X0: $i > $i,X1: $i,X2: $i] :
( ( in @ ( lam @ X2 @ X1 @ X0 ) @ ( funcSet @ X2 @ X1 ) )
| ( in @ ( sk__10 @ X0 @ X1 @ X2 ) @ X2 ) ),
inference(simplify,[status(thm)],[zip_derived_cl494]) ).
thf(zip_derived_cl11_006,plain,
~ ( in @ ( lam @ sk__11 @ sk__12 @ sk__13 ) @ ( funcSet @ sk__11 @ sk__12 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl513,plain,
in @ ( sk__10 @ sk__13 @ sk__12 @ sk__11 ) @ sk__11,
inference('sup-',[status(thm)],[zip_derived_cl504,zip_derived_cl11]) ).
thf(zip_derived_cl521,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl273,zip_derived_cl513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU680^2 : TPTP v9.2.0. Released v3.7.0.
% 0.11/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.rdRk4JlIOo true
% 0.11/0.32 % Computer : n005.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 16:15:23 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
% 0.17/0.63 % Total configuration time : 828
% 0.17/0.63 % Estimated wc time : 1656
% 0.17/0.63 % Estimated cpu time (8 cpus) : 207.0
% 1.22/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.22/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.22/0.71 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.22/0.71 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.39/0.72 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.39/0.72 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.39/0.72 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.39/0.73 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 11.01/2.01 % Solved by lams/40_noforms.sh.
% 11.01/2.01 % done 143 iterations in 1.246s
% 11.01/2.01 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 11.01/2.01 % SZS output start Refutation
% See solution above
% 11.01/2.01
% 11.01/2.01
% 11.01/2.01 % Terminating...
% 12.00/2.19 % Runner terminated.
% 12.00/2.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------