%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM636^4 : 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.dfIN175CSf true
% Computer : n004.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 04:47:44 PM UTC 2025
% Result : Theorem 279.60s 48.81s
% Output : Refutation 279.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 34
% Syntax : Number of formulae : 67 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 137 ( 52 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 288 ( 24 ~; 19 |; 0 &; 197 @)
% ( 0 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 5 con; 0-3 aty)
% Number of variables : 135 ( 57 ^; 78 !; 0 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
thf(zip_tseitin_7_type,type,
zip_tseitin_7: $i > ( $i > $o ) > $o ).
thf(nat_type,type,
nat: $i ).
thf(nat_p_type,type,
nat_p: $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('#l_lift20100_type',type,
'#l_lift20100': $o > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(sk__30_type,type,
sk__30: ( $i > $o ) > $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(omega_type,type,
omega: $i ).
thf('#l_lift20098_type',type,
'#l_lift20098': $i > $o ).
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(sk__44_type,type,
sk__44: $i ).
thf(esti_type,type,
esti: $i > $i > $i > $o ).
thf(sk__4_type,type,
sk__4: ( $i > $o ) > $i ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(def_nis,axiom,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_n_is,axiom,
( n_is
= ( e_is @ nat ) ) ).
thf(def_e_is,axiom,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ) ).
thf('0',plain,
( e_is
= ( ^ [X0: $i,X: $i,Y: $i] : ( X = Y ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_e_is]) ).
thf('1',plain,
( e_is
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( V_2 = V_3 ) ) ),
define([status(thm)]) ).
thf('2',plain,
( n_is
= ( e_is @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_is,'1']) ).
thf('3',plain,
( n_is
= ( e_is @ nat ) ),
define([status(thm)]) ).
thf(def_d_not,axiom,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ) ).
thf(def_imp,axiom,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ) ).
thf('4',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('5',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('6',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'5']) ).
thf('7',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('8',plain,
( nis
= ( ^ [X0: $i,X1: $i] : ( d_not @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nis,'3','1','7']) ).
thf('9',plain,
( nis
= ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( 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(def_is_of,axiom,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ) ).
thf('10',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('11',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('12',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,'11']) ).
thf('13',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(satz2,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] : ( nis @ ( ordsucc @ X0 ) @ X0 ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ( ( ordsucc @ X4 )
!= X4 ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ( ( ordsucc @ X4 )
!= X4 ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl185,plain,
( ( ordsucc @ sk__44 )
= sk__44 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(ordsucc_inj,axiom,
! [X0: $i,X1: $i] :
( ( ( ordsucc @ X0 )
= ( ordsucc @ X1 ) )
=> ( X0 = X1 ) ) ).
thf(zip_derived_cl48,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( ( ordsucc @ X1 )
!= ( ordsucc @ X0 ) ) ),
inference(cnf,[status(esa)],[ordsucc_inj]) ).
thf(zip_derived_cl364,plain,
! [X0: $i] :
( ( ( ordsucc @ X0 )
!= sk__44 )
| ( X0 = sk__44 ) ),
inference('sup-',[status(thm)],[zip_derived_cl185,zip_derived_cl48]) ).
thf(zip_derived_cl185_001,plain,
( ( ordsucc @ sk__44 )
= sk__44 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(def_nat_p,axiom,
( nat_p
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( X1 @ emptyset )
=> ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( ordsucc @ X2 ) ) )
=> ( X1 @ X0 ) ) ) ) ) ).
thf('14',plain,
( nat_p
= ( ^ [X0: $i] :
! [X1: $i > $o] :
( ( X1 @ emptyset )
=> ( ! [X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( ordsucc @ X2 ) ) )
=> ( X1 @ X0 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat_p]) ).
thf('15',plain,
( nat_p
= ( ^ [V_1: $i] :
! [X4: $i > $o] :
( ( X4 @ emptyset )
=> ( ! [X6: $i] :
( ( X4 @ X6 )
=> ( X4 @ ( ordsucc @ X6 ) ) )
=> ( X4 @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(omega_nat_p,axiom,
! [X0: $i] :
( ( in @ X0 @ omega )
=> ( nat_p @ X0 ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( in @ X4 @ omega )
=> ! [X6: $i > $o] :
( ( X6 @ emptyset )
=> ( ! [X8: $i] :
( ( X6 @ X8 )
=> ( X6 @ ( ordsucc @ X8 ) ) )
=> ( X6 @ X4 ) ) ) ) ).
thf(zip_derived_cl79,plain,
! [X0: $i > $o,X1: $i] :
( ~ ( X0 @ emptyset )
| ( X0 @ X1 )
| ( X0 @ ( sk__30 @ X0 ) )
| ~ ( in @ X1 @ omega ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(neq_ordsucc_0,axiom,
! [X0: $i] :
( ( ordsucc @ X0 )
!= emptyset ) ).
thf(zip_derived_cl47,plain,
! [X0: $i] :
( ( ordsucc @ X0 )
!= emptyset ),
inference(cnf,[status(esa)],[neq_ordsucc_0]) ).
thf(k_In_ind,axiom,
! [X0: $i > $o] :
( ! [X1: $i] :
( ! [X2: $i] :
( ( in @ X2 @ X1 )
=> ( X0 @ X2 ) )
=> ( X0 @ X1 ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ).
thf(zip_derived_cl5,plain,
! [X0: $i > $o,X1: $i] :
( ( X0 @ X1 )
| ~ ( X0 @ ( sk__4 @ X0 ) ) ),
inference(cnf,[status(esa)],[k_In_ind]) ).
thf(nat_ind,axiom,
! [X0: $i > $o] :
( ( X0 @ emptyset )
=> ( ! [X1: $i] :
( ( nat_p @ X1 )
=> ( ( X0 @ X1 )
=> ( X0 @ ( ordsucc @ X1 ) ) ) )
=> ! [X1: $i] :
( ( nat_p @ X1 )
=> ( X0 @ X1 ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i > $o] :
( ( X4 @ emptyset )
=> ( ! [X6: $i] :
( ! [X8: $i > $o] :
( ( X8 @ emptyset )
=> ( ! [X10: $i] :
( ( X8 @ X10 )
=> ( X8 @ ( ordsucc @ X10 ) ) )
=> ( X8 @ X6 ) ) )
=> ( ( X4 @ X6 )
=> ( X4 @ ( ordsucc @ X6 ) ) ) )
=> ! [X12: $i] :
( ! [X14: $i > $o] :
( ( X14 @ emptyset )
=> ( ! [X16: $i] :
( ( X14 @ X16 )
=> ( X14 @ ( ordsucc @ X16 ) ) )
=> ( X14 @ X12 ) ) )
=> ( X4 @ X12 ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X10: $i,X8: $i > $o] :
( ( ( X8 @ X10 )
=> ( X8 @ ( ordsucc @ X10 ) ) )
=> ( zip_tseitin_7 @ X10 @ X8 ) ) ).
thf(zip_derived_cl60,plain,
! [X0: $i,X1: $i > $o] :
( ( zip_tseitin_7 @ X0 @ X1 )
| ( X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl7641,plain,
! [X0: $o,X1: $i,X2: $i] :
( ( ^ [Y0: $i] : X0
@ X2 )
| ( zip_tseitin_7 @ X1
@ ^ [Y0: $i] : X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl5,zip_derived_cl60]) ).
thf(zip_derived_cl7680,plain,
! [X0: $o,X1: $i] :
( X0
| ( zip_tseitin_7 @ X1
@ ^ [Y0: $i] : X0 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl7641]) ).
thf(zip_derived_cl5_002,plain,
! [X0: $i > $o,X1: $i] :
( ( X0 @ X1 )
| ~ ( X0 @ ( sk__4 @ X0 ) ) ),
inference(cnf,[status(esa)],[k_In_ind]) ).
thf(zip_derived_cl59,plain,
! [X0: $i,X1: $i > $o] :
( ( zip_tseitin_7 @ X0 @ X1 )
| ~ ( X1 @ ( ordsucc @ X0 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl4137,plain,
! [X0: $o,X1: $i] :
( ~ ( ^ [Y0: $i] : X0
@ ( sk__4
@ ^ [Y0: $i] : X0 ) )
| ( zip_tseitin_7 @ X1
@ ^ [Y0: $i] : X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl5,zip_derived_cl59]) ).
thf(zip_derived_cl4172,plain,
! [X0: $o,X1: $i] :
( ~ X0
| ( zip_tseitin_7 @ X1
@ ^ [Y0: $i] : X0 ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl4137]) ).
thf(zip_derived_cl22245,plain,
! [X0: $o,X1: $i] :
( zip_tseitin_7 @ X1
@ ^ [Y0: $i] : X0 ),
inference(clc,[status(thm)],[zip_derived_cl7680,zip_derived_cl4172]) ).
thf(zip_derived_cl26044,plain,
! [X0: $o,X2: $i] :
( ( '#l_lift20100' @ X0 @ X2 )
= X0 ),
define([status(thm)]) ).
thf(zip_derived_cl184,plain,
in @ sk__44 @ nat,
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl78,plain,
! [X0: $i > $o,X1: $i] :
( ~ ( X0 @ emptyset )
| ( X0 @ X1 )
| ~ ( X0 @ ( ordsucc @ ( sk__30 @ X0 ) ) )
| ~ ( in @ X1 @ omega ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(def_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf(zip_derived_cl174,plain,
( nat
= ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[def_nat]) ).
thf(zip_derived_cl174_003,plain,
( nat
= ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[def_nat]) ).
thf(zip_derived_cl26038,plain,
! [X1: $i] :
( ( '#l_lift20098' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl26039,plain,
( nat
= ( d_Sep @ omega @ '#l_lift20098' ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl174,zip_derived_cl26038]) ).
thf(def_esti,axiom,
( esti
= ( ^ [X0: $i] : in ) ) ).
thf('16',plain,
( esti
= ( ^ [X0: $i] : in ) ),
inference(simplify_rw_rule,[status(thm)],[def_esti]) ).
thf('17',plain,
( esti
= ( ^ [V_1: $i] : in ) ),
define([status(thm)]) ).
thf(estii,axiom,
! [X0: $i,X1: $i > $o] :
( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ^ [X2: $i] :
( ( X1 @ X2 )
=> ( esti @ X0 @ X2 @ ( d_Sep @ X0 @ X1 ) ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i,X6: $i > $o,X8: $i] :
( ( in @ X8 @ X4 )
=> ( ( X6 @ X8 )
=> ( in @ X8 @ ( d_Sep @ X4 @ X6 ) ) ) ) ).
thf(zip_derived_cl154,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ~ ( X0 @ X1 )
| ( in @ X1 @ ( d_Sep @ X2 @ X0 ) )
| ~ ( in @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(k_SepE1,axiom,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ ( d_Sep @ X0 @ X1 ) )
=> ( in @ X2 @ X0 ) ) ).
thf(zip_derived_cl41,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
| ~ ( in @ X0 @ ( d_Sep @ X1 @ X2 ) ) ),
inference(cnf,[status(esa)],[k_SepE1]) ).
thf(zip_derived_cl26060,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl364,zip_derived_cl185,zip_derived_cl79,zip_derived_cl47,zip_derived_cl26044,zip_derived_cl184,zip_derived_cl78,zip_derived_cl26039,zip_derived_cl154,zip_derived_cl41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM636^4 : TPTP v9.2.0. Released v7.1.0.
% 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dfIN175CSf true
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Oct 1 16:22:53 EDT 2025
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.54/0.68 % Total configuration time : 828
% 0.54/0.68 % Estimated wc time : 1656
% 0.54/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.79 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.80 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.81 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.83 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.85 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 38.41/7.67 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 248.26/44.67 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 279.60/48.81 % Solved by lams/40_noforms.sh.
% 279.60/48.81 % done 1259 iterations in 47.965s
% 279.60/48.81 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 279.60/48.81 % SZS output start Refutation
% See solution above
% 279.60/48.81
% 279.60/48.81
% 279.60/48.81 % Terminating...
% 279.60/48.89 % Runner terminated.
% 279.60/48.90 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------