%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM667^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GQA6dUvNHz true
% Computer : n019.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 04:47:54 PM UTC 2025
% Result : Theorem 95.12s 17.16s
% Output : Refutation 95.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 40
% Syntax : Number of formulae : 66 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 84 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 418 ( 50 ~; 14 |; 0 &; 320 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 9 con; 0-3 aty)
% Number of variables : 137 ( 94 ^; 43 !; 0 ?; 137 :)
% Comments :
%------------------------------------------------------------------------------
thf(n_1_type,type,
n_1: $i ).
thf(nat_type,type,
nat: $i ).
thf(lessis_type,type,
lessis: $i > $i > $o ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(nis_type,type,
nis: $i > $i > $o ).
thf(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(sk__3_type,type,
sk__3: $i ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf('#l_lift2442_type',type,
'#l_lift2442': $i > $o ).
thf('#l_lift2441_type',type,
'#l_lift2441': $i > $i > $o ).
thf(sk__4_type,type,
sk__4: $i ).
thf(omega_type,type,
omega: $i ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(l_or_type,type,
l_or: $o > $o > $o ).
thf(ordsucc_type,type,
ordsucc: $i > $i ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(iii_type,type,
iii: $i > $i > $o ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('0',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('1',plain,
( nat
= ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('2',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('3',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'1','3']) ).
thf('5',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf(def_l_or,axiom,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
thf(def_imp,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ) ).
thf('6',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('7',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'7']) ).
thf('9',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('10',plain,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'9','7']) ).
thf('11',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('12',plain,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_lessis,'5','1','3','11','9','7']) ).
thf('13',plain,
( lessis
= ( ^ [V_1: $i,V_2: $i] : ( l_or @ ( iii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(def_all_of,axiom,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ) ).
thf('14',plain,
( all_of
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( is_of @ X2 @ X0 )
=> ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_all_of]) ).
thf('15',plain,
( all_of
= ( ^ [V_1: $i > $o,V_2: $i > $o] :
! [X4: $i] :
( ( is_of @ X4 @ V_1 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(satz17,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( lessis @ X0 @ X1 )
=> ( ( lessis @ X1 @ X2 )
=> ( lessis @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( ~ ( iii @ X4 @ X6 )
=> ( X4 = X6 ) )
=> ( ( ~ ( iii @ X6 @ X8 )
=> ( X6 = X8 ) )
=> ( ~ ( iii @ X4 @ X8 )
=> ( X4 = X8 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( ~ ( iii @ X4 @ X6 )
=> ( X4 = X6 ) )
=> ( ( ~ ( iii @ X6 @ X8 )
=> ( X6 = X8 ) )
=> ( ~ ( iii @ X4 @ X8 )
=> ( X4 = X8 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl60,plain,
sk__2 != sk__4,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl62,plain,
( ( sk__2 = sk__3 )
| ( iii @ sk__2 @ sk__3 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl59,plain,
( ( sk__3 = sk__4 )
| ( iii @ sk__3 @ sk__4 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl63,plain,
( is_of @ sk__3
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(refis,axiom,
! [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ X0 )
@ ^ [X1: $i] : ( e_is @ X0 @ X1 @ X1 ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: $i] :
( ( is_of @ X6
@ ^ [V_1: $i] : ( in @ V_1 @ X4 ) )
=> ( X6 = X6 ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( $true
| ~ ( is_of @ X0
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl4267,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf('16',plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_1]) ).
thf('17',plain,
( n_1
= ( ordsucc @ emptyset ) ),
define([status(thm)]) ).
thf(def_nis,axiom,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf('18',plain,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nis,'5','1','3','9','7']) ).
thf('19',plain,
( nis
= ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(n_ax3,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ n_1 ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ( ( ordsucc @ X4 )
!= ( ordsucc @ emptyset ) ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i] :
( ( ( ordsucc @ X0 )
!= ( ordsucc @ emptyset ) )
| ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl4270,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4321,plain,
is_of @ sk__3 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl63,zip_derived_cl4267,zip_derived_cl4270]) ).
thf(zip_derived_cl57,plain,
( is_of @ sk__2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4267_001,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl4270_002,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4319,plain,
is_of @ sk__2 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl57,zip_derived_cl4267,zip_derived_cl4270]) ).
thf(zip_derived_cl61,plain,
~ ( iii @ sk__2 @ sk__4 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl58,plain,
( is_of @ sk__4
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4267_003,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl4270_004,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4320,plain,
is_of @ sk__4 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl58,zip_derived_cl4267,zip_derived_cl4270]) ).
thf(satz16b,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ nat )
@ ^ [X2: $i] :
( ( iii @ X0 @ X1 )
=> ( ( lessis @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ( is_of @ X4
@ ^ [V_1: $i] :
( in @ V_1
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) )
=> ! [X6: $i] :
( ( is_of @ X6
@ ^ [V_3: $i] :
( in @ V_3
@ ( d_Sep @ omega
@ ^ [V_4: $i] : ( V_4 != emptyset ) ) ) )
=> ! [X8: $i] :
( ( is_of @ X8
@ ^ [V_5: $i] :
( in @ V_5
@ ( d_Sep @ omega
@ ^ [V_6: $i] : ( V_6 != emptyset ) ) ) )
=> ( ( iii @ X4 @ X6 )
=> ( ( ~ ( iii @ X6 @ X8 )
=> ( X6 = X8 ) )
=> ( iii @ X4 @ X8 ) ) ) ) ) ) ).
thf(zip_derived_cl51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( iii @ X1 @ X0 )
| ( iii @ X1 @ X2 )
| ~ ( iii @ X0 @ X2 )
| ~ ( is_of @ X2
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) )
| ~ ( is_of @ X1
@ ^ [Y0: $i] :
( in @ Y0
@ ( d_Sep @ omega
@ ^ [Y1: $i] : ( Y1 != emptyset ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl4267_005,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl4270_006,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4267_007,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl4270_008,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4267_009,plain,
! [X1: $i,X2: $i] :
( ( '#l_lift2441' @ X1 @ X2 )
= ( in @ X2 @ X1 ) ),
define([status(thm)]) ).
thf(zip_derived_cl4270_010,plain,
! [X1: $i] :
( ( '#l_lift2442' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl4313,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( is_of @ X0 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ) )
| ~ ( iii @ X1 @ X0 )
| ( iii @ X1 @ X2 )
| ~ ( iii @ X0 @ X2 )
| ~ ( is_of @ X2 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ) )
| ~ ( is_of @ X1 @ ( '#l_lift2441' @ ( d_Sep @ omega @ '#l_lift2442' ) ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl51,zip_derived_cl4267,zip_derived_cl4270,zip_derived_cl4267,zip_derived_cl4270,zip_derived_cl4267,zip_derived_cl4270]) ).
thf(zip_derived_cl4349,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl60,zip_derived_cl62,zip_derived_cl59,zip_derived_cl4321,zip_derived_cl4319,zip_derived_cl61,zip_derived_cl4320,zip_derived_cl4313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM667^4 : TPTP v9.2.0. Released v7.1.0.
% 0.13/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.GQA6dUvNHz true
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Wed Oct 1 16:16:53 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.15/0.37 % Running portfolio for 300 s
% 0.15/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.37 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.60/0.76 % Total configuration time : 828
% 0.60/0.76 % Estimated wc time : 1656
% 0.60/0.76 % Estimated cpu time (8 cpus) : 207.0
% 0.60/0.82 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.62/0.86 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.62/0.87 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.63/0.89 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.63/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.63/0.89 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.63/0.91 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.63/0.91 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 35.72/6.88 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 95.12/17.16 % Solved by lams/40_c.s.sh.
% 95.12/17.16 % done 378 iterations in 16.251s
% 95.12/17.16 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 95.12/17.16 % SZS output start Refutation
% See solution above
% 95.12/17.16
% 95.12/17.16
% 95.12/17.16 % Terminating...
% 95.63/17.38 % Runner terminated.
% 95.67/17.41 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------