TSTP Solution File: NUM701^4 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM701^4 : TPTP v8.1.2. Released v7.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Jnqa9jpoZh 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 Aug 31 12:43:35 EDT 2023
% Result : Theorem 129.11s 17.18s
% Output : Refutation 129.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 99
% Syntax : Number of formulae : 144 ( 61 unt; 25 typ; 0 def)
% Number of atoms : 528 ( 142 equ; 0 cnn)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 1156 ( 169 ~; 72 |; 0 &; 855 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 7 con; 0-3 aty)
% Number of variables : 250 ( 150 ^; 100 !; 0 ?; 250 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf(n_1_type,type,
n_1: $i ).
thf(nat_type,type,
nat: $i ).
thf(moreis_type,type,
moreis: $i > $i > $o ).
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('#l_lift12946_type',type,
'#l_lift12946': $i > $o ).
thf(nis_type,type,
nis: $i > $i > $o ).
thf(sk__3_type,type,
sk__3: $i ).
thf(d_Sep_type,type,
d_Sep: $i > ( $i > $o ) > $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(d_Sing_type,type,
d_Sing: $i > $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(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
thf(binunion_type,type,
binunion: $i > $i > $i ).
thf(n_some_type,type,
n_some: ( $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(sk__2_type,type,
sk__2: $i ).
thf(def_lessis,axiom,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_iii,axiom,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ).
thf('0',plain,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_iii]) ).
thf('1',plain,
( iii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_2 @ V_1 ) ) ) ),
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('2',plain,
( imp
= ( ^ [X0: $o,X1: $o] :
( X0
=> X1 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_imp]) ).
thf('3',plain,
( imp
= ( ^ [V_1: $o,V_2: $o] :
( V_1
=> V_2 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( d_not
= ( ^ [X0: $o] : ( imp @ X0 @ $false ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_not,'3']) ).
thf('5',plain,
( d_not
= ( ^ [V_1: $o] : ( imp @ V_1 @ $false ) ) ),
define([status(thm)]) ).
thf('6',plain,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'5','3']) ).
thf('7',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('8',plain,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_lessis,'1','7','5','3']) ).
thf('9',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_nat,axiom,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ) ).
thf('10',plain,
( nat
= ( d_Sep @ omega
@ ^ [X0: $i] : ( X0 != emptyset ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_nat]) ).
thf('11',plain,
( nat
= ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ),
define([status(thm)]) ).
thf(def_ordsucc,axiom,
( ordsucc
= ( ^ [X0: $i] : ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) ) ).
thf('12',plain,
( ordsucc
= ( ^ [X0: $i] : ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_ordsucc]) ).
thf('13',plain,
( ordsucc
= ( ^ [V_1: $i] : ( binunion @ V_1 @ ( d_Sing @ V_1 ) ) ) ),
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('14',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('15',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
thf('16',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,'15']) ).
thf('17',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(satz26a,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X1 @ ( ordsucc @ X0 ) )
=> ( lessis @ X1 @ X0 ) ) ) ) ).
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 ) ) )
=> ( ( n_some @ ( diffprop @ ( binunion @ X4 @ ( d_Sing @ X4 ) ) @ X6 ) )
=> ( ~ ( n_some @ ( diffprop @ X4 @ X6 ) )
=> ( n_is @ X6 @ X4 ) ) ) ) ) ).
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 ) ) )
=> ( ( n_some @ ( diffprop @ ( binunion @ X4 @ ( d_Sing @ X4 ) ) @ X6 ) )
=> ( ~ ( n_some @ ( diffprop @ X4 @ X6 ) )
=> ( n_is @ X6 @ X4 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl108,plain,
~ ( n_is @ sk__3 @ sk__2 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
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','3']) ).
thf('19',plain,
( nis
= ( ^ [V_1: $i,V_2: $i] : ( d_not @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz1,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( nis @ X0 @ X1 )
=> ( nis @ ( ordsucc @ X0 ) @ ( ordsucc @ X1 ) ) ) ) ) ).
thf(zf_stmt_2,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 ) ) )
=> ( ~ ( n_is @ X4 @ X6 )
=> ~ ( n_is @ ( binunion @ X4 @ ( d_Sing @ X4 ) ) @ ( binunion @ X6 @ ( d_Sing @ X6 ) ) ) ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( n_is @ ( binunion @ X1 @ ( d_Sing @ X1 ) ) @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) )
| ( n_is @ X1 @ X0 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf('20',plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_1,'13']) ).
thf('21',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_3,axiom,
( in @ ( binunion @ emptyset @ ( d_Sing @ emptyset ) )
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) ) ).
thf(zip_derived_cl12,plain,
( in @ ( binunion @ emptyset @ ( d_Sing @ emptyset ) )
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl8728,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_001,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8733,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( n_is @ ( binunion @ X1 @ ( d_Sing @ X1 ) ) @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) )
| ( n_is @ X1 @ X0 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl16,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz10h,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X0 @ X1 )
=> ( d_not @ ( moreis @ X0 @ X1 ) ) ) ) ) ).
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 ) ) )
=> ( ( n_some @ ( diffprop @ X6 @ X4 ) )
=> ~ ( moreis @ X4 @ X6 ) ) ) ) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( moreis @ X1 @ X0 )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl8728_002,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_003,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8762,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( moreis @ X1 @ X0 )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl44,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz18c,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] : ( iii @ X0 @ ( ordsucc @ X0 ) ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ( n_some @ ( diffprop @ ( binunion @ X4 @ ( d_Sing @ X4 ) ) @ X4 ) ) ) ).
thf(zip_derived_cl62,plain,
! [X0: $i] :
( ( n_some @ ( diffprop @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) @ X0 ) )
| ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl8728_004,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8776,plain,
! [X0: $i] :
( ( n_some @ ( diffprop @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) @ X0 ) )
| ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl62,zip_derived_cl8728]) ).
thf(satz16a,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] :
( ( lessis @ X0 @ X1 )
=> ( ( iii @ X1 @ X2 )
=> ( iii @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_6,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 ) ) )
=> ( ( ~ ( n_some @ ( diffprop @ X6 @ X4 ) )
=> ( n_is @ X4 @ X6 ) )
=> ( ( n_some @ ( diffprop @ X8 @ X6 ) )
=> ( n_some @ ( diffprop @ X8 @ X4 ) ) ) ) ) ) ) ).
thf(zip_derived_cl49,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( n_is @ X1 @ X0 )
| ( n_some @ ( diffprop @ X2 @ X1 ) )
| ~ ( n_some @ ( diffprop @ X2 @ X0 ) )
| ~ ( in @ X2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl8728_005,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_006,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_007,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( n_is @ X1 @ X0 )
| ( n_some @ ( diffprop @ X2 @ X1 ) )
| ~ ( n_some @ ( diffprop @ X2 @ X0 ) )
| ~ ( in @ X2 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl49,zip_derived_cl8728,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(zip_derived_cl107,plain,
n_some @ ( diffprop @ ( binunion @ sk__2 @ ( d_Sing @ sk__2 ) ) @ sk__3 ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(satz25c,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X1 @ X0 )
=> ( lessis @ ( ordsucc @ X1 ) @ X0 ) ) ) ) ).
thf(zf_stmt_7,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 ) ) )
=> ( ( n_some @ ( diffprop @ X4 @ X6 ) )
=> ( ~ ( n_some @ ( diffprop @ X4 @ ( binunion @ X6 @ ( d_Sing @ X6 ) ) ) )
=> ( n_is @ ( binunion @ X6 @ ( d_Sing @ X6 ) ) @ X4 ) ) ) ) ) ).
thf(zip_derived_cl104,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( n_some @ ( diffprop @ X1 @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) )
| ( n_is @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) @ X1 )
| ~ ( n_some @ ( diffprop @ X1 @ X0 ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_7]) ).
thf(zip_derived_cl8728_008,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_009,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8816,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ( n_some @ ( diffprop @ X1 @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) ) )
| ( n_is @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) @ X1 )
| ~ ( n_some @ ( diffprop @ X1 @ X0 ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl104,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz25a,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_29_ii @ X1 @ X0 )
=> ( moreis @ X1 @ ( ordsucc @ X0 ) ) ) ) ) ).
thf(zf_stmt_8,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 ) ) )
=> ( ( d_29_ii @ X6 @ X4 )
=> ( moreis @ X6 @ ( binunion @ X4 @ ( d_Sing @ X4 ) ) ) ) ) ) ).
thf(zip_derived_cl102,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( moreis @ X0 @ ( binunion @ X1 @ ( d_Sing @ X1 ) ) )
| ~ ( d_29_ii @ X0 @ X1 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_8]) ).
thf(zip_derived_cl8728_010,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_011,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8814,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ( moreis @ X0 @ ( binunion @ X1 @ ( d_Sing @ X1 ) ) )
| ~ ( d_29_ii @ X0 @ X1 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl102,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz10g,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( d_not @ ( lessis @ X0 @ X1 ) ) ) ) ) ).
thf(zf_stmt_9,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 ) ) )
=> ( ( d_29_ii @ X4 @ X6 )
=> ~ ( ~ ( n_some @ ( diffprop @ X6 @ X4 ) )
=> ( n_is @ X4 @ X6 ) ) ) ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( n_is @ X1 @ X0 )
| ~ ( d_29_ii @ X1 @ X0 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_9]) ).
thf(zip_derived_cl8728_012,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_013,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8761,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( n_is @ X1 @ X0 )
| ~ ( d_29_ii @ X1 @ X0 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl43,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(zip_derived_cl106,plain,
( in @ sk__2
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8728_014,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8818,plain,
in @ sk__2 @ ( d_Sep @ omega @ '#l_lift12946' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl106,zip_derived_cl8728]) ).
thf(zip_derived_cl42,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( d_29_ii @ X1 @ X0 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_9]) ).
thf(zip_derived_cl8728_015,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_016,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8760,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( d_29_ii @ X1 @ X0 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl42,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(zip_derived_cl109,plain,
~ ( n_some @ ( diffprop @ sk__2 @ sk__3 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl110,plain,
( in @ sk__3
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl8728_017,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8819,plain,
in @ sk__3 @ ( d_Sep @ omega @ '#l_lift12946' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl110,zip_derived_cl8728]) ).
thf(satz13,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( moreis @ X0 @ X1 )
=> ( lessis @ X1 @ X0 ) ) ) ) ).
thf(zf_stmt_10,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 ) ) )
=> ( ( moreis @ X4 @ X6 )
=> ( ~ ( n_some @ ( diffprop @ X4 @ X6 ) )
=> ( n_is @ X6 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl34,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( n_some @ ( diffprop @ X1 @ X0 ) )
| ( n_is @ X0 @ X1 )
| ~ ( moreis @ X1 @ X0 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_10]) ).
thf(zip_derived_cl8728_018,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_019,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8752,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ( n_some @ ( diffprop @ X1 @ X0 ) )
| ( n_is @ X0 @ X1 )
| ~ ( moreis @ X1 @ X0 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl34,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz12,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X0 @ X1 )
=> ( d_29_ii @ X1 @ X0 ) ) ) ) ).
thf(zf_stmt_11,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 ) ) )
=> ( ( n_some @ ( diffprop @ X6 @ X4 ) )
=> ( d_29_ii @ X6 @ X4 ) ) ) ) ).
thf(zip_derived_cl33,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( d_29_ii @ X0 @ X1 )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_11]) ).
thf(zip_derived_cl8728_020,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_021,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8751,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ( d_29_ii @ X0 @ X1 )
| ~ ( n_some @ ( diffprop @ X0 @ X1 ) )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl33,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(suc_p,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( is_of @ ( ordsucc @ X0 )
@ ^ [X1: $i] : ( in @ X1 @ nat ) ) ) ).
thf(zf_stmt_12,axiom,
! [X4: $i] :
( ( in @ X4
@ ( d_Sep @ omega
@ ^ [V_1: $i] : ( V_1 != emptyset ) ) )
=> ( in @ ( binunion @ X4 @ ( d_Sing @ X4 ) )
@ ( d_Sep @ omega
@ ^ [V_2: $i] : ( V_2 != emptyset ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i] :
( ( in @ ( binunion @ X0 @ ( d_Sing @ X0 ) )
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_12]) ).
thf(zip_derived_cl8728_022,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_023,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8730,plain,
! [X0: $i] :
( ( in @ ( binunion @ X0 @ ( d_Sing @ X0 ) ) @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl13,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(satz10j,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( d_not @ ( moreis @ X0 @ X1 ) )
=> ( iii @ X0 @ X1 ) ) ) ) ).
thf(zf_stmt_13,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 ) ) )
=> ( ~ ( moreis @ X4 @ X6 )
=> ( n_some @ ( diffprop @ X6 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl45,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) )
| ( n_some @ ( diffprop @ X0 @ X1 ) )
| ( moreis @ X1 @ X0 )
| ~ ( in @ X1
@ ( d_Sep @ omega
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_13]) ).
thf(zip_derived_cl8728_024,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8728_025,plain,
! [X1: $i] :
( ( '#l_lift12946' @ X1 )
= ( X1 != emptyset ) ),
define([status(thm)]) ).
thf(zip_derived_cl8763,plain,
! [X0: $i,X1: $i] :
( ~ ( in @ X0 @ ( d_Sep @ omega @ '#l_lift12946' ) )
| ( n_some @ ( diffprop @ X0 @ X1 ) )
| ( moreis @ X1 @ X0 )
| ~ ( in @ X1 @ ( d_Sep @ omega @ '#l_lift12946' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl45,zip_derived_cl8728,zip_derived_cl8728]) ).
thf(zip_derived_cl8877,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl108,zip_derived_cl8733,zip_derived_cl8762,zip_derived_cl8776,zip_derived_cl8767,zip_derived_cl107,zip_derived_cl8816,zip_derived_cl8814,zip_derived_cl8761,zip_derived_cl8818,zip_derived_cl8760,zip_derived_cl109,zip_derived_cl8819,zip_derived_cl8752,zip_derived_cl8751,zip_derived_cl8730,zip_derived_cl8763]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM701^4 : TPTP v8.1.2. Released v7.1.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Jnqa9jpoZh true
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 09:02:09 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.54/0.65 % Total configuration time : 828
% 0.54/0.65 % Estimated wc time : 1656
% 0.54/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.70 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 129.11/17.17 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 129.11/17.18 % Solved by lams/40_c.s.sh.
% 129.11/17.18 % done 719 iterations in 16.404s
% 129.11/17.18 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 129.11/17.18 % SZS output start Refutation
% See solution above
% 129.11/17.18
% 129.11/17.18
% 129.11/17.18 % Terminating...
% 129.75/17.28 % Runner terminated.
% 129.75/17.29 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------