TSTP Solution File: NUM698^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM698^4 : 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.uWQgRof1ox true
% Computer : n025.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 12:43:34 EDT 2023
% Result : Theorem 144.65s 19.59s
% Output : Refutation 144.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 89
% Syntax : Number of formulae : 171 ( 80 unt; 31 typ; 0 def)
% Number of atoms : 791 ( 241 equ; 42 cnn)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 1816 ( 249 ~; 71 |; 0 &;1140 @)
% ( 0 <=>; 241 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 9 con; 0-3 aty)
% ( 115 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 350 ( 261 ^; 89 !; 0 ?; 350 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf(n_1_type,type,
n_1: $i ).
thf(orec3_type,type,
orec3: $o > $o > $o > $o ).
thf(nat_type,type,
nat: $i ).
thf(moreis_type,type,
moreis: $i > $i > $o ).
thf(lessis_type,type,
lessis: $i > $i > $o ).
thf(and3_type,type,
and3: $o > $o > $o > $o ).
thf(is_of_type,type,
is_of: $i > ( $i > $o ) > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(non_type,type,
non: $i > ( $i > $o ) > $i > $o ).
thf(l_some_type,type,
l_some: $i > ( $i > $o ) > $o ).
thf('#sk8366_type',type,
'#sk8366': $i ).
thf(emptyset_type,type,
emptyset: $i ).
thf(n_is_type,type,
n_is: $i > $i > $o ).
thf(l_ec_type,type,
l_ec: $o > $o > $o ).
thf(imp_type,type,
imp: $o > $o > $o ).
thf(ec3_type,type,
ec3: $o > $o > $o > $o ).
thf('#sk4715_type',type,
'#sk4715': $i ).
thf('#sk8365_type',type,
'#sk8365': $i ).
thf(d_and_type,type,
d_and: $o > $o > $o ).
thf(all_of_type,type,
all_of: ( $i > $o ) > ( $i > $o ) > $o ).
thf(diffprop_type,type,
diffprop: $i > $i > $i > $o ).
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('#form7857_type',type,
'#form7857': $i > $i > $o ).
thf(or3_type,type,
or3: $o > $o > $o > $o ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $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(def_diffprop,axiom,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ) ).
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('4',plain,
( diffprop
= ( ^ [X0: $i,X1: $i,X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_diffprop,'3','1']) ).
thf('5',plain,
( diffprop
= ( ^ [V_1: $i,V_2: $i,V_3: $i] : ( n_is @ V_1 @ ( n_pl @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(def_n_some,axiom,
( n_some
= ( l_some @ nat ) ) ).
thf(def_l_some,axiom,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ) ).
thf(def_non,axiom,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ) ).
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,
( non
= ( ^ [X0: $i,X1: $i > $o,X2: $i] : ( d_not @ ( X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_non,'9','7']) ).
thf('11',plain,
( non
= ( ^ [V_1: $i,V_2: $i > $o,V_3: $i] : ( d_not @ ( V_2 @ V_3 ) ) ) ),
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('12',plain,
( is_of
= ( ^ [X0: $i,X1: $i > $o] : ( X1 @ X0 ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_is_of]) ).
thf('13',plain,
( is_of
= ( ^ [V_1: $i,V_2: $i > $o] : ( V_2 @ V_1 ) ) ),
define([status(thm)]) ).
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,'13']) ).
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('16',plain,
( l_some
= ( ^ [X0: $i,X1: $i > $o] :
( d_not
@ ( all_of
@ ^ [X2: $i] : ( in @ X2 @ X0 )
@ ( non @ X0 @ X1 ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_some,'11','9','7','15','13']) ).
thf('17',plain,
( l_some
= ( ^ [V_1: $i,V_2: $i > $o] :
( d_not
@ ( all_of
@ ^ [V_3: $i] : ( in @ V_3 @ V_1 )
@ ( non @ V_1 @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('18',plain,
( n_some
= ( l_some @ nat ) ),
inference(simplify_rw_rule,[status(thm)],[def_n_some,'17','11','9','7','15','13']) ).
thf('19',plain,
( n_some
= ( l_some @ nat ) ),
define([status(thm)]) ).
thf('20',plain,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_iii,'5','19','3','1','17','11','9','7','15','13']) ).
thf('21',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('22',plain,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'9','7']) ).
thf('23',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('24',plain,
( lessis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( iii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_lessis,'21','5','19','3','1','17','11','23','9','7','15','13']) ).
thf('25',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(satz25b,conjecture,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( ( iii @ X1 @ X0 )
=> ( lessis @ ( n_pl @ X1 @ n_1 ) @ X0 ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X8 ) ) )
=> ( ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X6 @ n_1 ) @ X10 ) ) )
=> ( ( n_pl @ X6 @ n_1 )
= X4 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X8 ) ) )
=> ( ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X6 @ n_1 ) @ X10 ) ) )
=> ( ( n_pl @ X6 @ n_1 )
= X4 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl199,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ ( n_pl @ Y1 @ n_1 ) @ Y2 ) ) ) )
=> ( ( n_pl @ Y1 @ n_1 )
= Y0 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl6885,plain,
~ ( ( in @ '#sk8365' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8365'
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ Y0 @ n_1 ) @ Y1 ) ) ) )
=> ( ( n_pl @ Y0 @ n_1 )
= '#sk8365' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl199]) ).
thf(zip_derived_cl6887,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8365'
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ Y0 @ n_1 ) @ Y1 ) ) ) )
=> ( ( n_pl @ Y0 @ n_1 )
= '#sk8365' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6885]) ).
thf(zip_derived_cl6888,plain,
~ ( ( in @ '#sk8366' @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ '#sk8366' @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ '#sk8366' @ n_1 ) @ Y0 ) ) ) )
=> ( ( n_pl @ '#sk8366' @ n_1 )
= '#sk8365' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6887]) ).
thf(def_n_1,axiom,
( n_1
= ( ordsucc @ emptyset ) ) ).
thf(zip_derived_cl108,plain,
( n_1
= ( ordsucc @ emptyset ) ),
inference(cnf,[status(esa)],[def_n_1]) ).
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_cl1,plain,
( !!
@ ^ [Y0: $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( Y0 @ Y2 ) ) )
=> ( Y0 @ Y1 ) ) )
=> ( !!
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf,[status(esa)],[k_In_ind]) ).
thf(zip_derived_cl303,plain,
! [X2: $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( X2 @ Y1 ) ) )
=> ( X2 @ Y0 ) ) )
=> ( !!
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl542,plain,
( ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( Y1 != emptyset ) ) )
=> ( Y0 != emptyset ) ) )
=> ( !!
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl303]) ).
thf(zip_derived_cl3723,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( Y1 != emptyset ) ) )
=> ( Y0 != emptyset ) ) )
| ( !!
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl542]) ).
thf(zip_derived_cl3724,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ '#sk4715' )
=> ( Y0 != emptyset ) ) )
=> ( '#sk4715' != emptyset ) )
| ( !!
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3723]) ).
thf(zip_derived_cl3726,plain,
( ( '#sk4715' != emptyset )
| ( !!
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl3724]) ).
thf(zip_derived_cl3728,plain,
( ( '#sk4715' = emptyset )
| ( !!
@ ^ [Y0: $i] : ( Y0 != emptyset ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl3726]) ).
thf(zip_derived_cl3729,plain,
! [X2: $i] :
( ( X2 != emptyset )
| ( '#sk4715' = emptyset ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3728]) ).
thf(zip_derived_cl3731,plain,
! [X2: $i] :
( ( X2 != emptyset )
| ( '#sk4715' = emptyset ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl3729]) ).
thf(zip_derived_cl3732,plain,
'#sk4715' = emptyset,
inference(simplify,[status(thm)],[zip_derived_cl3731]) ).
thf(zip_derived_cl3739,plain,
( n_1
= ( ordsucc @ '#sk4715' ) ),
inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl3732]) ).
thf(zip_derived_cl6889,plain,
~ ( ( in @ '#sk8366' @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ '#sk8366' @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ '#sk8366' @ n_1 ) @ Y0 ) ) ) )
=> ( ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) )
= '#sk8365' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl6888,zip_derived_cl3739]) ).
thf(zip_derived_cl6891,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ '#sk8366' @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ '#sk8366' @ n_1 ) @ Y0 ) ) ) )
=> ( ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) )
= '#sk8365' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6889]) ).
thf(zip_derived_cl6893,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ '#sk8366' @ n_1 ) @ Y0 ) ) ) )
=> ( ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) )
= '#sk8365' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6891]) ).
thf(zip_derived_cl6895,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ ( n_pl @ '#sk8366' @ n_1 ) @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6893]) ).
thf(def_orec3,axiom,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ) ).
thf(def_ec3,axiom,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ) ).
thf(def_and3,axiom,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ) ).
thf(def_d_and,axiom,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ) ).
thf(def_l_ec,axiom,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ) ).
thf('26',plain,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_ec,'9','7']) ).
thf('27',plain,
( l_ec
= ( ^ [V_1: $o,V_2: $o] : ( imp @ V_1 @ ( d_not @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('28',plain,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_and,'27','9','7']) ).
thf('29',plain,
( d_and
= ( ^ [V_1: $o,V_2: $o] : ( d_not @ ( l_ec @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('30',plain,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_and3,'29','27','9','7']) ).
thf('31',plain,
( and3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ V_1 @ ( d_and @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('32',plain,
( ec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( and3 @ ( l_ec @ X0 @ X1 ) @ ( l_ec @ X1 @ X2 ) @ ( l_ec @ X2 @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_ec3,'31','29','27','9','7']) ).
thf('33',plain,
( ec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( and3 @ ( l_ec @ V_1 @ V_2 ) @ ( l_ec @ V_2 @ V_3 ) @ ( l_ec @ V_3 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(def_or3,axiom,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ) ).
thf('34',plain,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_or3,'23','9','7']) ).
thf('35',plain,
( or3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( l_or @ V_1 @ ( l_or @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('36',plain,
( orec3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ ( or3 @ X0 @ X1 @ X2 ) @ ( ec3 @ X0 @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_orec3,'33','31','35','23','29','27','9','7']) ).
thf('37',plain,
( orec3
= ( ^ [V_1: $o,V_2: $o,V_3: $o] : ( d_and @ ( or3 @ V_1 @ V_2 @ V_3 ) @ ( ec3 @ V_1 @ V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(satz9,axiom,
( all_of
@ ^ [X0: $i] : ( in @ X0 @ nat )
@ ^ [X0: $i] :
( all_of
@ ^ [X1: $i] : ( in @ X1 @ nat )
@ ^ [X1: $i] :
( orec3 @ ( n_is @ X0 @ X1 )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X0 @ ( n_pl @ X1 @ X2 ) ) )
@ ( n_some
@ ^ [X2: $i] : ( n_is @ X1 @ ( n_pl @ X0 @ X2 ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ~ ( ( ( X4 != X6 )
=> ( ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X8 ) ) )
=> ~ ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X10 ) ) ) ) )
=> ( ( ( X4 = X6 )
=> ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X12 ) ) ) )
=> ( ( ~ ! [X14: $i] :
( ( in @ X14 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X14 ) ) )
=> ! [X16: $i] :
( ( in @ X16 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X16 ) ) ) )
=> ~ ( ~ ! [X18: $i] :
( ( in @ X18 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X18 ) ) )
=> ( X4 != X6 ) ) ) ) ) ) ) ).
thf(zip_derived_cl137,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( (~)
@ ( ( ( Y0 != Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) ) ) )
=> ( ( ( Y0 = Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( Y0 != Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl6236,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( (~)
@ ( ( ( X2 != Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( X2 = Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( X2 != Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl6237,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( (~)
@ ( ( ( X2 != Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) ) ) )
=> ( ( ( X2 = Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( X2 != Y0 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6236]) ).
thf(zip_derived_cl6238,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( (~)
@ ( ( ( X2 != X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6237]) ).
thf(zip_derived_cl6239,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ~ ( ( ( X2 != X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
=> ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6238]) ).
thf(zip_derived_cl6241,plain,
! [X2: $i,X4: $i] :
( ~ ( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6239]) ).
thf(zip_derived_cl6243,plain,
! [X2: $i,X4: $i] :
( ( ( X2 = X4 )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6241]) ).
thf(zip_derived_cl6247,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6243]) ).
thf(zip_derived_cl6253,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6247]) ).
thf(zip_derived_cl6254,plain,
! [X4: $i] :
( ~ ( in @ X4 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl6253]) ).
thf(zip_derived_cl6255,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6240,plain,
! [X2: $i,X4: $i] :
( ( ( X2 != X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6239]) ).
thf(zip_derived_cl6242,plain,
! [X2: $i,X4: $i] :
( ( X2 != X4 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6240]) ).
thf(zip_derived_cl6245,plain,
! [X2: $i,X4: $i] :
( ( X2 = X4 )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6242]) ).
thf(zip_derived_cl6246,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ( X2 = X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6245]) ).
thf(zip_derived_cl6250,plain,
! [X2: $i,X4: $i] :
( ( '#form7857' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6897,plain,
'#form7857' @ '#sk8365' @ ( n_pl @ '#sk8366' @ n_1 ),
inference(renaming,[status(thm)],[zip_derived_cl6895,zip_derived_cl6255,zip_derived_cl6250]) ).
thf(zip_derived_cl3739_001,plain,
( n_1
= ( ordsucc @ '#sk4715' ) ),
inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl3732]) ).
thf(zip_derived_cl6899,plain,
'#form7857' @ '#sk8365' @ ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) ),
inference(demod,[status(thm)],[zip_derived_cl6897,zip_derived_cl3739]) ).
thf(def_moreis,axiom,
( moreis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ) ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).
thf('38',plain,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_29_ii,'5','19','3','1','17','11','9','7','15','13']) ).
thf('39',plain,
( d_29_ii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('40',plain,
( moreis
= ( ^ [X0: $i,X1: $i] : ( l_or @ ( d_29_ii @ X0 @ X1 ) @ ( n_is @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_moreis,'39','5','19','3','1','17','11','23','9','7','15','13']) ).
thf('41',plain,
( moreis
= ( ^ [V_1: $i,V_2: $i] : ( l_or @ ( d_29_ii @ V_1 @ V_2 ) @ ( n_is @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz25,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 @ ( n_pl @ X0 @ n_1 ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ( ~ ! [X8: $i] :
( ( in @ X8 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X8 ) ) )
=> ( ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( X6
!= ( n_pl @ ( n_pl @ X4 @ n_1 ) @ X10 ) ) )
=> ( X6
= ( n_pl @ X4 @ n_1 ) ) ) ) ) ) ).
thf(zip_derived_cl197,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ ( n_pl @ Y0 @ n_1 ) @ Y2 ) ) ) )
=> ( Y1
= ( n_pl @ Y0 @ n_1 ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl12845,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y1 ) ) ) )
=> ( Y0
= ( n_pl @ X2 @ n_1 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl12846,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ X2 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y1 ) ) ) )
=> ( Y0
= ( n_pl @ X2 @ n_1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12845]) ).
thf(zip_derived_cl12847,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
=> ( X4
= ( n_pl @ X2 @ n_1 ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12846]) ).
thf(zip_derived_cl3739_002,plain,
( n_1
= ( ordsucc @ '#sk4715' ) ),
inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl3732]) ).
thf(zip_derived_cl12848,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
=> ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(demod,[status(thm)],[zip_derived_cl12847,zip_derived_cl3739]) ).
thf(zip_derived_cl12849,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
=> ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12848]) ).
thf(zip_derived_cl12850,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
=> ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12849]) ).
thf(zip_derived_cl6255_003,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6250_004,plain,
! [X2: $i,X4: $i] :
( ( '#form7857' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12851,plain,
! [X2: $i,X4: $i] :
( ( '#form7857' @ X4 @ X2 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
=> ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl12850,zip_derived_cl6255,zip_derived_cl6250]) ).
thf(zip_derived_cl12852,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
| ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ( '#form7857' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12851]) ).
thf(zip_derived_cl12853,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ ( n_pl @ X2 @ n_1 ) @ Y0 ) ) ) )
| ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ( '#form7857' @ X4 @ X2 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl12852]) ).
thf(zip_derived_cl6255_005,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6250_006,plain,
! [X2: $i,X4: $i] :
( ( '#form7857' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12854,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X4 @ ( n_pl @ X2 @ n_1 ) )
| ( '#form7857' @ X4 @ X2 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl12853,zip_derived_cl6255,zip_derived_cl6250]) ).
thf(zip_derived_cl3739_007,plain,
( n_1
= ( ordsucc @ '#sk4715' ) ),
inference(demod,[status(thm)],[zip_derived_cl108,zip_derived_cl3732]) ).
thf(zip_derived_cl12855,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X4 @ ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) )
| ( '#form7857' @ X4 @ X2 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( X4
= ( n_pl @ X2 @ ( ordsucc @ '#sk4715' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12854,zip_derived_cl3739]) ).
thf(zip_derived_cl12876,plain,
( ( '#sk8365'
= ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) ) )
| ~ ( in @ '#sk8366' @ nat )
| ~ ( in @ '#sk8365' @ nat )
| ( '#form7857' @ '#sk8365' @ '#sk8366' ) ),
inference('sup-',[status(thm)],[zip_derived_cl6899,zip_derived_cl12855]) ).
thf(zip_derived_cl6890,plain,
in @ '#sk8366' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6889]) ).
thf(zip_derived_cl6886,plain,
in @ '#sk8365' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6885]) ).
thf(zip_derived_cl6892,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk8365'
!= ( n_pl @ '#sk8366' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6891]) ).
thf(zip_derived_cl6255_008,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form7857' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6250_009,plain,
! [X2: $i,X4: $i] :
( ( '#form7857' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl6894,plain,
~ ( '#form7857' @ '#sk8365' @ '#sk8366' ),
inference(renaming,[status(thm)],[zip_derived_cl6892,zip_derived_cl6255,zip_derived_cl6250]) ).
thf(zip_derived_cl12893,plain,
( '#sk8365'
= ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl12876,zip_derived_cl6890,zip_derived_cl6886,zip_derived_cl6894]) ).
thf(zip_derived_cl6896,plain,
( ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) )
!= '#sk8365' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6893]) ).
thf(zip_derived_cl6898,plain,
( ( n_pl @ '#sk8366' @ ( ordsucc @ '#sk4715' ) )
!= '#sk8365' ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl6896]) ).
thf(zip_derived_cl12894,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl12893,zip_derived_cl6898]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : NUM698^4 : TPTP v8.1.2. Released v7.1.0.
% 0.10/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.uWQgRof1ox true
% 0.11/0.36 % Computer : n025.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Aug 25 09:54:37 EDT 2023
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Running portfolio for 300 s
% 0.11/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.36 % Number of cores: 8
% 0.16/0.36 % Python version: Python 3.6.8
% 0.16/0.37 % Running in HO mode
% 0.17/0.66 % Total configuration time : 828
% 0.17/0.66 % Estimated wc time : 1656
% 0.17/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.17/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.17/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.17/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.17/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.17/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.17/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.17/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.98/0.80 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 144.65/19.59 % Solved by lams/35_full_unif4.sh.
% 144.65/19.59 % done 1117 iterations in 18.801s
% 144.65/19.59 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 144.65/19.59 % SZS output start Refutation
% See solution above
% 144.65/19.59
% 144.65/19.59
% 144.65/19.59 % Terminating...
% 146.15/19.71 % Runner terminated.
% 146.15/19.71 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------