%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM647^4 : TPTP v9.2.0. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.0CiTcV41Cb true
% Computer : n003.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 04:47:48 PM UTC 2025
% Result : Theorem 143.24s 19.15s
% Output : Refutation 143.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 36
% Syntax : Number of formulae : 61 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 196 ( 88 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 365 ( 48 ~; 12 |; 0 &; 283 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 8 con; 0-3 aty)
% Number of variables : 112 ( 80 ^; 32 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(n_1_type,type,
n_1: $i ).
thf(sk__2_type,type,
sk__2: $i ).
thf(nat_type,type,
nat: $i ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(sk__3_type,type,
sk__3: $i ).
thf(nis_type,type,
nis: $i > $i > $o ).
thf(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(ap_type,type,
ap: $i > $i > $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf('#l_lift12255_type',type,
'#l_lift12255': $i > $o ).
thf(omega_type,type,
omega: $i ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(ordsucc_type,type,
ordsucc: $i > $i ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(plus_type,type,
plus: $i > $i ).
thf(sk__4_type,type,
sk__4: $i ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_n_pl,axiom,
( n_pl
= ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ) ).
thf('0',plain,
( n_pl
= ( ^ [X0: $i] : ( ap @ ( plus @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_pl]) ).
thf('1',plain,
( n_pl
= ( ^ [V_1: $i] : ( ap @ ( plus @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('2',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('3',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('4',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('5',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('6',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'3','5']) ).
thf('7',plain,
( n_is
= ( e_is @ nat ) ),
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(def_is_of,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
thf('8',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('9',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('10',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,'9']) ).
thf('11',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(satz8a,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] :
( ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) )
=> ( n_is @ X1 @ X2 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ! [X8: $i] :
( ( in @ X8
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) ) )
=> ( ( ( ap @ ( plus @ X4 ) @ X6 )
= ( ap @ ( plus @ X4 ) @ X8 ) )
=> ( X6 = X8 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ! [X8: $i] :
( ( in @ X8
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) ) )
=> ( ( ( ap @ ( plus @ X4 ) @ X6 )
= ( ap @ ( plus @ X4 ) @ X8 ) )
=> ( X6 = X8 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl34,plain,
sk__3 != sk__4,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl36,plain,
( in @ sk__3
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf('12',plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_1]) ).
thf('13',plain,
( n_1
= ( ordsucc @ emptyset ) ),
define([status(thm)]) ).
thf(n_1_p,axiom,
( is_of @ n_1
@ ^ [X0: $i] : ( in @ X0 @ nat ) ) ).
thf(zf_stmt_2,axiom,
( in @ ( ordsucc @ emptyset )
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ) ).
thf(zip_derived_cl14,plain,
( in @ ( ordsucc @ emptyset )
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl9556,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9577,plain,
in @ sk__3 @ ( d_Sep @ omega @ '#l_lift12255' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl36,zip_derived_cl9556]) ).
thf(def_nis,axiom,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
thf(def_imp,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ) ).
thf('14',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('15',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('16',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'15']) ).
thf('17',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('18',plain,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nis,'7','3','5','17','15']) ).
thf('19',plain,
( nis
= ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz8,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] :
( ( nis @ X1 @ X2 )
=> ( nis @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ! [X8: $i] :
( ( in @ X8
@ ( d_Sep @ omega
@ ^ [V_3: $i] : ( V_3 != emptyset ) ) )
=> ( ( X6 != X8 )
=> ( ( ap @ ( plus @ X4 ) @ X6 )
!= ( ap @ ( plus @ X4 ) @ X8 ) ) ) ) ) ) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( X0 = X1 )
| ( ( ap @ ( plus @ X2 ) @ X0 )
!= ( ap @ ( plus @ X2 ) @ X1 ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( in @ X2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl9556_001,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9556_002,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9556_003,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9574,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12255' ) )
| ( X0 = X1 )
| ( ( ap @ ( plus @ X2 ) @ X0 )
!= ( ap @ ( plus @ X2 ) @ X1 ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12255' ) )
| ~ ( in @ X2 @ ( d_Sep @ omega @ '#l_lift12255' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl31,zip_derived_cl9556,zip_derived_cl9556,zip_derived_cl9556]) ).
thf(zip_derived_cl33,plain,
( in @ sk__4
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl9556_004,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9576,plain,
in @ sk__4 @ ( d_Sep @ omega @ '#l_lift12255' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl33,zip_derived_cl9556]) ).
thf(zip_derived_cl32,plain,
( in @ sk__2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl9556_005,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9575,plain,
in @ sk__2 @ ( d_Sep @ omega @ '#l_lift12255' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl32,zip_derived_cl9556]) ).
thf(zip_derived_cl35,plain,
( ( ap @ ( plus @ sk__2 ) @ sk__3 )
= ( ap @ ( plus @ sk__2 ) @ sk__4 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(satz6,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] : ( n_is @ ( n_pl @ X0 @ X1 ) @ ( n_pl @ X1 @ X0 ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ! [X6: $i] :
( ( in @ X6
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) )
=> ( ( ap @ ( plus @ X4 ) @ X6 )
= ( ap @ ( plus @ X6 ) @ X4 ) ) ) ) ).
thf(zip_derived_cl29,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( ( ap @ ( plus @ X1 ) @ X0 )
= ( ap @ ( plus @ X0 ) @ X1 ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl9556_006,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9556_007,plain,
! [X1: $i] :
( ( '#l_lift12255' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl9572,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12255' ) )
| ( ( ap @ ( plus @ X1 ) @ X0 )
= ( ap @ ( plus @ X0 ) @ X1 ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12255' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl29,zip_derived_cl9556,zip_derived_cl9556]) ).
thf(zip_derived_cl9601,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl34,zip_derived_cl9577,zip_derived_cl9574,zip_derived_cl9576,zip_derived_cl9575,zip_derived_cl35,zip_derived_cl9572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM647^4 : TPTP v9.2.0. Released v7.1.0.
% 0.06/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.0CiTcV41Cb true
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 1 16:17:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in HO mode
% 0.52/0.65 % Total configuration time : 828
% 0.52/0.65 % Estimated wc time : 1656
% 0.52/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.52/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.53/0.78 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.80 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.54/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 30.33/4.92 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 143.24/19.15 % Solved by lams/40_c.s.sh.
% 143.24/19.15 % done 499 iterations in 18.359s
% 143.24/19.15 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 143.24/19.15 % SZS output start Refutation
% See solution above
% 143.24/19.15
% 143.24/19.15
% 143.24/19.15 % Terminating...
% 144.10/19.31 % Runner terminated.
% 144.10/19.32 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------