TSTP Solution File: NUM721^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : NUM721^4 : 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.inCZgMRi3G true
% Computer : n016.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 12:43:43 EDT 2023
% Result : Theorem 180.00s 23.99s
% Output : Refutation 180.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 85
% Syntax : Number of formulae : 157 ( 65 unt; 29 typ; 0 def)
% Number of atoms : 985 ( 235 equ; 94 cnn)
% Maximal formula atoms : 30 ( 7 avg)
% Number of connectives : 2504 ( 376 ~; 97 |; 0 &;1540 @)
% ( 0 <=>; 324 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 8 con; 0-3 aty)
% ( 167 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 434 ( 309 ^; 125 !; 0 ?; 434 :)
% Comments :
%------------------------------------------------------------------------------
thf(d_29_ii_type,type,
d_29_ii: $i > $i > $o ).
thf('#sk15128_type',type,
'#sk15128': $i ).
thf('#sk15125_type',type,
'#sk15125': $i ).
thf(orec3_type,type,
orec3: $o > $o > $o > $o ).
thf('#sk15127_type',type,
'#sk15127': $i ).
thf(nat_type,type,
nat: $i ).
thf('#sk8476_type',type,
'#sk8476': $i > $i > $i ).
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(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(n_ts_type,type,
n_ts: $i > $i > $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('#sk15126_type',type,
'#sk15126': $i ).
thf(n_some_type,type,
n_some: ( $i > $o ) > $o ).
thf(l_or_type,type,
l_or: $o > $o > $o ).
thf(d_not_type,type,
d_not: $o > $o ).
thf(iii_type,type,
iii: $i > $i > $o ).
thf(or3_type,type,
or3: $o > $o > $o > $o ).
thf(e_is_type,type,
e_is: $i > $i > $i > $o ).
thf('#form8477_type',type,
'#form8477': $i > $i > $o ).
thf(n_pl_type,type,
n_pl: $i > $i > $i ).
thf(def_d_29_ii,axiom,
( d_29_ii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X0 @ X1 ) ) ) ) ).
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,
( 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('21',plain,
( d_29_ii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(satz34,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] :
( all_of
@ ^ [X3: $i] : ( in @ X3 @ nat )
@ ^ [X3: $i] :
( ( d_29_ii @ X0 @ X1 )
=> ( ( d_29_ii @ X2 @ X3 )
=> ( d_29_ii @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X3 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( X4
!= ( n_pl @ X6 @ X12 ) ) )
=> ( ~ ! [X14: $i] :
( ( in @ X14 @ nat )
=> ( X8
!= ( n_pl @ X10 @ X14 ) ) )
=> ~ ! [X16: $i] :
( ( in @ X16 @ nat )
=> ( ( n_ts @ X4 @ X8 )
!= ( n_pl @ ( n_ts @ X6 @ X10 ) @ X16 ) ) ) ) ) ) ) ) ) ).
thf(zip_derived_cl240,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y4 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( Y2
!= ( n_pl @ Y3 @ Y4 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( ( n_ts @ Y0 @ Y2 )
!= ( n_pl @ ( n_ts @ Y1 @ Y3 ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl15031,plain,
! [X2: $i] :
( ( in @ X2 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y3 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y1
!= ( n_pl @ Y2 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_ts @ X2 @ Y1 )
!= ( n_pl @ ( n_ts @ Y0 @ Y2 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl240]) ).
thf(zip_derived_cl15032,plain,
! [X2: $i] :
( ~ ( in @ X2 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( X2
!= ( n_pl @ Y0 @ Y3 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y1
!= ( n_pl @ Y2 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_ts @ X2 @ Y1 )
!= ( n_pl @ ( n_ts @ Y0 @ Y2 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15031]) ).
thf(zip_derived_cl15033,plain,
! [X2: $i,X4: $i] :
( ( ( in @ X4 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y2 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_ts @ X2 @ Y0 )
!= ( n_pl @ ( n_ts @ X4 @ Y1 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15032]) ).
thf(zip_derived_cl15034,plain,
! [X2: $i,X4: $i] :
( ~ ( in @ X4 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y2 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y0
!= ( n_pl @ Y1 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_ts @ X2 @ Y0 )
!= ( n_pl @ ( n_ts @ X4 @ Y1 ) @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15033]) ).
thf(zip_derived_cl15035,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y1 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X6
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15034]) ).
thf(zip_derived_cl15036,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( in @ X6 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y1 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( X6
!= ( n_pl @ Y0 @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ Y0 ) @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15035]) ).
thf(zip_derived_cl15037,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( in @ X8 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X6
!= ( n_pl @ X8 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15036]) ).
thf(zip_derived_cl15038,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( in @ X8 @ nat )
| ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X6
!= ( n_pl @ X8 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) ) ) ) )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15037]) ).
thf(zip_derived_cl15039,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X2
!= ( n_pl @ X4 @ Y0 ) ) ) )
| ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X6
!= ( n_pl @ X8 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X8 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15038]) ).
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('22',plain,
( l_ec
= ( ^ [X0: $o,X1: $o] : ( imp @ X0 @ ( d_not @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_ec,'9','7']) ).
thf('23',plain,
( l_ec
= ( ^ [V_1: $o,V_2: $o] : ( imp @ V_1 @ ( d_not @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('24',plain,
( d_and
= ( ^ [X0: $o,X1: $o] : ( d_not @ ( l_ec @ X0 @ X1 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_d_and,'23','9','7']) ).
thf('25',plain,
( d_and
= ( ^ [V_1: $o,V_2: $o] : ( d_not @ ( l_ec @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf('26',plain,
( and3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( d_and @ X0 @ ( d_and @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_and3,'25','23','9','7']) ).
thf('27',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('28',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,'27','25','23','9','7']) ).
thf('29',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(def_l_or,axiom,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ) ).
thf('30',plain,
( l_or
= ( ^ [X0: $o] : ( imp @ ( d_not @ X0 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_l_or,'9','7']) ).
thf('31',plain,
( l_or
= ( ^ [V_1: $o] : ( imp @ ( d_not @ V_1 ) ) ) ),
define([status(thm)]) ).
thf('32',plain,
( or3
= ( ^ [X0: $o,X1: $o,X2: $o] : ( l_or @ X0 @ ( l_or @ X1 @ X2 ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[def_or3,'31','9','7']) ).
thf('33',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('34',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,'29','27','33','31','25','23','9','7']) ).
thf('35',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_1,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_1]) ).
thf(zip_derived_cl7082,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_cl7083,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_cl7082]) ).
thf(zip_derived_cl7084,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_cl7083]) ).
thf(zip_derived_cl7085,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_cl7084]) ).
thf(zip_derived_cl7087,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_cl7085]) ).
thf(zip_derived_cl7090,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 ) ) ) ) )
=> ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) )
=> ( X2 != X4 ) ) ) )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7087]) ).
thf(zip_derived_cl7094,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 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7090]) ).
thf(zip_derived_cl7100,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 @ X4 @ nat )
| ~ ( in @ X2 @ nat ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7094]) ).
thf(zip_derived_cl7105,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( in @ X6 @ nat )
=> ( X2
!= ( n_pl @ X4 @ X6 ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7100]) ).
thf(zip_derived_cl7115,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7086,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_cl7085]) ).
thf(zip_derived_cl7088,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_cl7086]) ).
thf(zip_derived_cl7091,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_cl7088]) ).
thf(zip_derived_cl7092,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_cl7091]) ).
thf(zip_derived_cl7096,plain,
! [X2: $i,X4: $i] :
( ~ ( ( in @ ( '#sk8476' @ X2 @ X4 ) @ nat )
=> ( X2
!= ( n_pl @ X4 @ ( '#sk8476' @ X2 @ X4 ) ) ) )
| ( X2 = X4 )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7092]) ).
thf(zip_derived_cl7102,plain,
! [X2: $i,X4: $i] :
( ( in @ ( '#sk8476' @ X2 @ X4 ) @ nat )
| ~ ( !!
@ ^ [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_cl7096]) ).
thf(zip_derived_cl7109,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15040,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( '#form8477' @ X4 @ X2 )
| ~ ( in @ X8 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X6
!= ( n_pl @ X8 @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl15039,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(zip_derived_cl15041,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X6
!= ( n_pl @ X8 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X8 @ nat )
| ( '#form8477' @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15040]) ).
thf(zip_derived_cl7115_001,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7109_002,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15042,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( '#form8477' @ X8 @ X6 )
| ( '#form8477' @ X4 @ X2 )
| ~ ( in @ X8 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X2 @ nat )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ X2 @ X6 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl15041,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(zip_derived_cl7115_003,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7109_004,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15043,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( '#form8477' @ ( n_ts @ X4 @ X8 ) @ ( n_ts @ X2 @ X6 ) )
| ~ ( in @ X2 @ nat )
| ~ ( in @ X4 @ nat )
| ~ ( in @ X6 @ nat )
| ~ ( in @ X8 @ nat )
| ( '#form8477' @ X4 @ X2 )
| ( '#form8477' @ X8 @ X6 ) ),
inference(renaming,[status(thm)],[zip_derived_cl15042,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(def_iii,axiom,
( iii
= ( ^ [X0: $i,X1: $i] : ( n_some @ ( diffprop @ X1 @ X0 ) ) ) ) ).
thf('36',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('37',plain,
( iii
= ( ^ [V_1: $i,V_2: $i] : ( n_some @ ( diffprop @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(satz34a,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] :
( all_of
@ ^ [X3: $i] : ( in @ X3 @ nat )
@ ^ [X3: $i] :
( ( iii @ X0 @ X1 )
=> ( ( iii @ X2 @ X3 )
=> ( iii @ ( n_ts @ X0 @ X2 ) @ ( n_ts @ X1 @ X3 ) ) ) ) ) ) ) ) ).
thf(zf_stmt_2,conjecture,
! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X12 ) ) )
=> ( ~ ! [X14: $i] :
( ( in @ X14 @ nat )
=> ( X10
!= ( n_pl @ X8 @ X14 ) ) )
=> ~ ! [X16: $i] :
( ( in @ X16 @ nat )
=> ( ( n_ts @ X6 @ X10 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ X16 ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_3,negated_conjecture,
~ ! [X4: $i] :
( ( in @ X4 @ nat )
=> ! [X6: $i] :
( ( in @ X6 @ nat )
=> ! [X8: $i] :
( ( in @ X8 @ nat )
=> ! [X10: $i] :
( ( in @ X10 @ nat )
=> ( ~ ! [X12: $i] :
( ( in @ X12 @ nat )
=> ( X6
!= ( n_pl @ X4 @ X12 ) ) )
=> ( ~ ! [X14: $i] :
( ( in @ X14 @ nat )
=> ( X10
!= ( n_pl @ X8 @ X14 ) ) )
=> ~ ! [X16: $i] :
( ( in @ X16 @ nat )
=> ( ( n_ts @ X6 @ X10 )
!= ( n_pl @ ( n_ts @ X4 @ X8 ) @ X16 ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl241,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y4 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( Y3
!= ( n_pl @ Y2 @ Y4 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( in @ Y4 @ nat )
=> ( ( n_ts @ Y1 @ Y3 )
!= ( n_pl @ ( n_ts @ Y0 @ Y2 ) @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl15400,plain,
~ ( ( in @ '#sk15125' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y0
!= ( n_pl @ '#sk15125' @ Y3 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y2
!= ( n_pl @ Y1 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_ts @ Y0 @ Y2 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ Y1 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl241]) ).
thf(zip_derived_cl15402,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y0
!= ( n_pl @ '#sk15125' @ Y3 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( Y2
!= ( n_pl @ Y1 @ Y3 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( in @ Y3 @ nat )
=> ( ( n_ts @ Y0 @ Y2 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ Y1 ) @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15400]) ).
thf(zip_derived_cl15403,plain,
~ ( ( in @ '#sk15126' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y2 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_ts @ '#sk15126' @ Y1 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15402]) ).
thf(zip_derived_cl15405,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y2 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( Y1
!= ( n_pl @ Y0 @ Y2 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( in @ Y2 @ nat )
=> ( ( n_ts @ '#sk15126' @ Y1 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ Y0 ) @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15403]) ).
thf(zip_derived_cl15406,plain,
~ ( ( in @ '#sk15127' @ nat )
=> ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y1 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ '#sk15127' @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_ts @ '#sk15126' @ Y0 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15405]) ).
thf(zip_derived_cl15408,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y1 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( Y0
!= ( n_pl @ '#sk15127' @ Y1 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( in @ Y1 @ nat )
=> ( ( n_ts @ '#sk15126' @ Y0 )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15406]) ).
thf(zip_derived_cl15409,plain,
~ ( ( in @ '#sk15128' @ nat )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y0 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15128'
!= ( n_pl @ '#sk15127' @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ '#sk15126' @ '#sk15128' )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15408]) ).
thf(zip_derived_cl15411,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y0 ) ) ) ) )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15128'
!= ( n_pl @ '#sk15127' @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ '#sk15126' @ '#sk15128' )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15409]) ).
thf(zip_derived_cl15413,plain,
~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15128'
!= ( n_pl @ '#sk15127' @ Y0 ) ) ) ) )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ '#sk15126' @ '#sk15128' )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15411]) ).
thf(zip_derived_cl15416,plain,
( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( ( n_ts @ '#sk15126' @ '#sk15128' )
!= ( n_pl @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15413]) ).
thf(zip_derived_cl7115_005,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7109_006,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15418,plain,
'#form8477' @ ( n_ts @ '#sk15125' @ '#sk15127' ) @ ( n_ts @ '#sk15126' @ '#sk15128' ),
inference(renaming,[status(thm)],[zip_derived_cl15416,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(zip_derived_cl17147,plain,
( ( '#form8477' @ '#sk15127' @ '#sk15128' )
| ( '#form8477' @ '#sk15125' @ '#sk15126' )
| ~ ( in @ '#sk15127' @ nat )
| ~ ( in @ '#sk15128' @ nat )
| ~ ( in @ '#sk15125' @ nat )
| ~ ( in @ '#sk15126' @ nat ) ),
inference('sup+',[status(thm)],[zip_derived_cl15043,zip_derived_cl15418]) ).
thf(zip_derived_cl15415,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15128'
!= ( n_pl @ '#sk15127' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15413]) ).
thf(zip_derived_cl7115_007,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7109_008,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15417,plain,
~ ( '#form8477' @ '#sk15127' @ '#sk15128' ),
inference(renaming,[status(thm)],[zip_derived_cl15415,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(zip_derived_cl15412,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( '#sk15126'
!= ( n_pl @ '#sk15125' @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15411]) ).
thf(zip_derived_cl7115_009,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8477' @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl7109_010,plain,
! [X2: $i,X4: $i] :
( ( '#form8477' @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( in @ Y0 @ nat )
=> ( X4
!= ( n_pl @ X2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl15414,plain,
~ ( '#form8477' @ '#sk15125' @ '#sk15126' ),
inference(renaming,[status(thm)],[zip_derived_cl15412,zip_derived_cl7115,zip_derived_cl7109]) ).
thf(zip_derived_cl15407,plain,
in @ '#sk15127' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15406]) ).
thf(zip_derived_cl15410,plain,
in @ '#sk15128' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15409]) ).
thf(zip_derived_cl15401,plain,
in @ '#sk15125' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15400]) ).
thf(zip_derived_cl15404,plain,
in @ '#sk15126' @ nat,
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15403]) ).
thf(zip_derived_cl17156,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl17147,zip_derived_cl15417,zip_derived_cl15414,zip_derived_cl15407,zip_derived_cl15410,zip_derived_cl15401,zip_derived_cl15404]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : NUM721^4 : TPTP v8.1.2. Released v7.1.0.
% 0.00/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.inCZgMRi3G true
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 10:44:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.68 % Total configuration time : 828
% 0.22/0.68 % Estimated wc time : 1656
% 0.22/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 1.24/0.78 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.24/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.24/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.24/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 1.24/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 1.24/0.82 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.24/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 180.00/23.99 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 180.00/23.99 % Solved by lams/35_full_unif4.sh.
% 180.00/23.99 % done 1202 iterations in 23.154s
% 180.00/23.99 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 180.00/23.99 % SZS output start Refutation
% See solution above
% 180.00/23.99
% 180.00/23.99
% 180.00/23.99 % Terminating...
% 180.00/24.14 % Runner terminated.
% 180.00/24.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------