%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : ALG251^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.O7AbLhuUNj true
% Computer : n014.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 : Wed Aug 30 17:12:27 EDT 2023
% Result : Theorem 49.01s 6.98s
% Output : Refutation 49.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 98
% Syntax : Number of formulae : 170 ( 64 unt; 42 typ; 0 def)
% Number of atoms : 1704 ( 390 equ; 43 cnn)
% Maximal formula atoms : 88 ( 13 avg)
% Number of connectives : 5267 ( 121 ~; 17 |; 0 &;3389 @)
% ( 0 <=>; 925 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 9 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 40 usr; 34 con; 0-2 aty)
% ( 815 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1086 ( 834 ^; 252 !; 0 ?;1086 :)
% Comments :
%------------------------------------------------------------------------------
thf(term_type,type,
term: $tType ).
thf(subst_type,type,
subst: $tType ).
thf(axmap_type,type,
axmap: $o ).
thf(axclos_type,type,
axclos: $o ).
thf(lam_type,type,
lam: term > term ).
thf(lamnotap_type,type,
lamnotap: $o ).
thf(axvarcons_type,type,
axvarcons: $o ).
thf(pushprop_gthm_type,type,
pushprop_gthm: $o ).
thf('#l_lift15327_type',type,
'#l_lift15327': term > $o ).
thf(push_type,type,
push: term > subst > subst ).
thf('#sk48_type',type,
'#sk48': ( term > $o ) > term ).
thf(axshiftcons_type,type,
axshiftcons: $o ).
thf(axapp_type,type,
axapp: $o ).
thf(shinj_type,type,
shinj: $o ).
thf('#sk39_type',type,
'#sk39': term ).
thf('#sk10_type',type,
'#sk10': ( term > $o ) > term ).
thf(one_type,type,
one: term ).
thf(id_type,type,
id: subst ).
thf(comp_type,type,
comp: subst > subst > subst ).
thf(axvarid_type,type,
axvarid: $o ).
thf(axvarshift_type,type,
axvarshift: $o ).
thf(sh_type,type,
sh: subst ).
thf(laminj_type,type,
laminj: $o ).
thf(ulamvarind_type,type,
ulamvarind: $o ).
thf('#sk49_type',type,
'#sk49': subst ).
thf(apinj2_type,type,
apinj2: $o ).
thf(ulamvarsh_type,type,
ulamvarsh: $o ).
thf('#sk30_type',type,
'#sk30': term > $o ).
thf(lamnotvar_type,type,
lamnotvar: $o ).
thf(apnotvar_type,type,
apnotvar: $o ).
thf(pushprop_type,type,
pushprop: $o ).
thf(sub_type,type,
sub: term > subst > term ).
thf(apinj1_type,type,
apinj1: $o ).
thf(axidl_type,type,
axidl: $o ).
thf(ap_type,type,
ap: term > term > term ).
thf(var_type,type,
var: term > $o ).
thf(axassoc_type,type,
axassoc: $o ).
thf(axidr_type,type,
axidr: $o ).
thf(axabs_type,type,
axabs: $o ).
thf(ulamvar1_type,type,
ulamvar1: $o ).
thf(induction_type,type,
induction: $o ).
thf(axscons_type,type,
axscons: $o ).
thf(pushprop_gthm,axiom,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf('0',plain,
( pushprop_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> pushprop ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(pushprop,axiom,
( pushprop
= ( ! [P: term > $o,A: term,M: subst] :
( ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ M ) ) )
=> ( ( P @ A )
=> ! [B: term] :
( ( var @ B )
=> ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ) ) ).
thf('1',plain,
( pushprop
= ( ! [X4: term > $o,X6: term,X8: subst] :
( ! [X10: term] :
( ( var @ X10 )
=> ( X4 @ ( sub @ X10 @ X8 ) ) )
=> ( ( X4 @ X6 )
=> ! [X12: term] :
( ( var @ X12 )
=> ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(induction,axiom,
( induction
= ( ! [P: term > $o] :
( ! [A: term] :
( ( var @ A )
=> ( P @ A ) )
=> ( ! [A: term,B: term] :
( ( P @ A )
=> ( ( P @ B )
=> ( P @ ( ap @ A @ B ) ) ) )
=> ( ! [A: term] :
( ( P @ A )
=> ( P @ ( lam @ A ) ) )
=> ! [A: term] : ( P @ A ) ) ) ) ) ) ).
thf('2',plain,
( induction
= ( ! [X4: term > $o] :
( ! [X6: term] :
( ( var @ X6 )
=> ( X4 @ X6 ) )
=> ( ! [X8: term,X10: term] :
( ( X4 @ X8 )
=> ( ( X4 @ X10 )
=> ( X4 @ ( ap @ X8 @ X10 ) ) ) )
=> ( ! [X12: term] :
( ( X4 @ X12 )
=> ( X4 @ ( lam @ X12 ) ) )
=> ! [X14: term] : ( X4 @ X14 ) ) ) ) ) ),
define([status(thm)]) ).
thf(lamnotvar,axiom,
( lamnotvar
= ( ! [A: term] :
~ ( var @ ( lam @ A ) ) ) ) ).
thf('3',plain,
( lamnotvar
= ( ! [X4: term] :
~ ( var @ ( lam @ X4 ) ) ) ),
define([status(thm)]) ).
thf(apnotvar,axiom,
( apnotvar
= ( ! [A: term,B: term] :
~ ( var @ ( ap @ A @ B ) ) ) ) ).
thf('4',plain,
( apnotvar
= ( ! [X4: term,X6: term] :
~ ( var @ ( ap @ X4 @ X6 ) ) ) ),
define([status(thm)]) ).
thf(lamnotap,axiom,
( lamnotap
= ( ! [A: term,B: term,C: term] :
( ( lam @ A )
!= ( ap @ B @ C ) ) ) ) ).
thf('5',plain,
( lamnotap
= ( ! [X4: term,X6: term,X8: term] :
( ( lam @ X4 )
!= ( ap @ X6 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(shinj,axiom,
( shinj
= ( ! [A: term,B: term] :
( ( ( sub @ A @ sh )
= ( sub @ B @ sh ) )
=> ( A = B ) ) ) ) ).
thf('6',plain,
( shinj
= ( ! [X4: term,X6: term] :
( ( ( sub @ X4 @ sh )
= ( sub @ X6 @ sh ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(laminj,axiom,
( laminj
= ( ! [A: term,B: term] :
( ( ( lam @ A )
= ( lam @ B ) )
=> ( A = B ) ) ) ) ).
thf('7',plain,
( laminj
= ( ! [X4: term,X6: term] :
( ( ( lam @ X4 )
= ( lam @ X6 ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(apinj2,axiom,
( apinj2
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( C = D ) ) ) ) ).
thf('8',plain,
( apinj2
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( ap @ X4 @ X8 )
= ( ap @ X6 @ X10 ) )
=> ( X8 = X10 ) ) ) ),
define([status(thm)]) ).
thf(apinj1,axiom,
( apinj1
= ( ! [A: term,B: term,C: term,D: term] :
( ( ( ap @ A @ C )
= ( ap @ B @ D ) )
=> ( A = B ) ) ) ) ).
thf('9',plain,
( apinj1
= ( ! [X4: term,X6: term,X8: term,X10: term] :
( ( ( ap @ X4 @ X8 )
= ( ap @ X6 @ X10 ) )
=> ( X4 = X6 ) ) ) ),
define([status(thm)]) ).
thf(ulamvarind,axiom,
( ulamvarind
= ( ! [P: term > $o] :
( ( P @ one )
=> ( ! [A: term] :
( ( var @ A )
=> ( ( P @ A )
=> ( P @ ( sub @ A @ sh ) ) ) )
=> ! [A: term] :
( ( var @ A )
=> ( P @ A ) ) ) ) ) ) ).
thf('10',plain,
( ulamvarind
= ( ! [X4: term > $o] :
( ( X4 @ one )
=> ( ! [X6: term] :
( ( var @ X6 )
=> ( ( X4 @ X6 )
=> ( X4 @ ( sub @ X6 @ sh ) ) ) )
=> ! [X8: term] :
( ( var @ X8 )
=> ( X4 @ X8 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ulamvarsh,axiom,
( ulamvarsh
= ( ! [A: term] :
( ( var @ A )
=> ( var @ ( sub @ A @ sh ) ) ) ) ) ).
thf('11',plain,
( ulamvarsh
= ( ! [X4: term] :
( ( var @ X4 )
=> ( var @ ( sub @ X4 @ sh ) ) ) ) ),
define([status(thm)]) ).
thf(ulamvar1,axiom,
( ulamvar1
= ( var @ one ) ) ).
thf('12',plain,
( ulamvar1
= ( var @ one ) ),
inference(simplify_rw_rule,[status(thm)],[ulamvar1]) ).
thf('13',plain,
( ulamvar1
= ( var @ one ) ),
define([status(thm)]) ).
thf(axscons,axiom,
( axscons
= ( ! [M: subst] :
( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) )
= M ) ) ) ).
thf('14',plain,
( axscons
= ( ! [X4: subst] :
( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(axvarshift,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ) ).
thf('15',plain,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
define([status(thm)]) ).
thf(axidr,axiom,
( axidr
= ( ! [M: subst] :
( ( comp @ M @ id )
= M ) ) ) ).
thf('16',plain,
( axidr
= ( ! [X4: subst] :
( ( comp @ X4 @ id )
= X4 ) ) ),
define([status(thm)]) ).
thf(axmap,axiom,
( axmap
= ( ! [A: term,M: subst,N: subst] :
( ( comp @ ( push @ A @ M ) @ N )
= ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ) ) ) ).
thf('17',plain,
( axmap
= ( ! [X4: term,X6: subst,X8: subst] :
( ( comp @ ( push @ X4 @ X6 ) @ X8 )
= ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axassoc,axiom,
( axassoc
= ( ! [M: subst,N: subst,K: subst] :
( ( comp @ ( comp @ M @ N ) @ K )
= ( comp @ M @ ( comp @ N @ K ) ) ) ) ) ).
thf('18',plain,
( axassoc
= ( ! [X4: subst,X6: subst,X8: subst] :
( ( comp @ ( comp @ X4 @ X6 ) @ X8 )
= ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axshiftcons,axiom,
( axshiftcons
= ( ! [A: term,M: subst] :
( ( comp @ sh @ ( push @ A @ M ) )
= M ) ) ) ).
thf('19',plain,
( axshiftcons
= ( ! [X4: term,X6: subst] :
( ( comp @ sh @ ( push @ X4 @ X6 ) )
= X6 ) ) ),
define([status(thm)]) ).
thf(axidl,axiom,
( axidl
= ( ! [M: subst] :
( ( comp @ id @ M )
= M ) ) ) ).
thf('20',plain,
( axidl
= ( ! [X4: subst] :
( ( comp @ id @ X4 )
= X4 ) ) ),
define([status(thm)]) ).
thf(axclos,axiom,
( axclos
= ( ! [A: term,M: subst,N: subst] :
( ( sub @ ( sub @ A @ M ) @ N )
= ( sub @ A @ ( comp @ M @ N ) ) ) ) ) ).
thf('21',plain,
( axclos
= ( ! [X4: term,X6: subst,X8: subst] :
( ( sub @ ( sub @ X4 @ X6 ) @ X8 )
= ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(axabs,axiom,
( axabs
= ( ! [A: term,M: subst] :
( ( sub @ ( lam @ A ) @ M )
= ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ) ) ) ).
thf('22',plain,
( axabs
= ( ! [X4: term,X6: subst] :
( ( sub @ ( lam @ X4 ) @ X6 )
= ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(axvarid,axiom,
( axvarid
= ( ! [A: term] :
( ( sub @ A @ id )
= A ) ) ) ).
thf('23',plain,
( axvarid
= ( ! [X4: term] :
( ( sub @ X4 @ id )
= X4 ) ) ),
define([status(thm)]) ).
thf(axvarcons,axiom,
( axvarcons
= ( ! [A: term,M: subst] :
( ( sub @ one @ ( push @ A @ M ) )
= A ) ) ) ).
thf('24',plain,
( axvarcons
= ( ! [X4: term,X6: subst] :
( ( sub @ one @ ( push @ X4 @ X6 ) )
= X4 ) ) ),
define([status(thm)]) ).
thf(axapp,axiom,
( axapp
= ( ! [A: term,B: term,M: subst] :
( ( sub @ ( ap @ A @ B ) @ M )
= ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ) ) ) ).
thf('25',plain,
( axapp
= ( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) ),
define([status(thm)]) ).
thf(thm,conjecture,
pushprop_gthm ).
thf(zf_stmt_0,conjecture,
( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) )
=> ( ! [X10: term,X12: subst] :
( ( sub @ one @ ( push @ X10 @ X12 ) )
= X10 )
=> ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
=> ( ! [X16: term,X18: subst] :
( ( sub @ ( lam @ X16 ) @ X18 )
= ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) )
=> ( ! [X20: term,X22: subst,X24: subst] :
( ( sub @ ( sub @ X20 @ X22 ) @ X24 )
= ( sub @ X20 @ ( comp @ X22 @ X24 ) ) )
=> ( ! [X26: subst] :
( ( comp @ id @ X26 )
= X26 )
=> ( ! [X28: term,X30: subst] :
( ( comp @ sh @ ( push @ X28 @ X30 ) )
= X30 )
=> ( ! [X32: subst,X34: subst,X36: subst] :
( ( comp @ ( comp @ X32 @ X34 ) @ X36 )
= ( comp @ X32 @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: term,X40: subst,X42: subst] :
( ( comp @ ( push @ X38 @ X40 ) @ X42 )
= ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) )
=> ( ! [X44: subst] :
( ( comp @ X44 @ id )
= X44 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X46: subst] :
( ( push @ ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) )
= X46 )
=> ( ( var @ one )
=> ( ! [X48: term] :
( ( var @ X48 )
=> ( var @ ( sub @ X48 @ sh ) ) )
=> ( ! [X50: term > $o] :
( ( X50 @ one )
=> ( ! [X52: term] :
( ( var @ X52 )
=> ( ( X50 @ X52 )
=> ( X50 @ ( sub @ X52 @ sh ) ) ) )
=> ! [X54: term] :
( ( var @ X54 )
=> ( X50 @ X54 ) ) ) )
=> ( ! [X56: term,X58: term,X60: term,X62: term] :
( ( ( ap @ X56 @ X60 )
= ( ap @ X58 @ X62 ) )
=> ( X56 = X58 ) )
=> ( ! [X64: term,X66: term,X68: term,X70: term] :
( ( ( ap @ X64 @ X68 )
= ( ap @ X66 @ X70 ) )
=> ( X68 = X70 ) )
=> ( ! [X72: term,X74: term] :
( ( ( lam @ X72 )
= ( lam @ X74 ) )
=> ( X72 = X74 ) )
=> ( ! [X76: term,X78: term] :
( ( ( sub @ X76 @ sh )
= ( sub @ X78 @ sh ) )
=> ( X76 = X78 ) )
=> ( ! [X80: term,X82: term,X84: term] :
( ( lam @ X80 )
!= ( ap @ X82 @ X84 ) )
=> ( ! [X86: term,X88: term] :
~ ( var @ ( ap @ X86 @ X88 ) )
=> ( ! [X90: term] :
~ ( var @ ( lam @ X90 ) )
=> ( ! [X92: term > $o] :
( ! [X94: term] :
( ( var @ X94 )
=> ( X92 @ X94 ) )
=> ( ! [X96: term,X98: term] :
( ( X92 @ X96 )
=> ( ( X92 @ X98 )
=> ( X92 @ ( ap @ X96 @ X98 ) ) ) )
=> ( ! [X100: term] :
( ( X92 @ X100 )
=> ( X92 @ ( lam @ X100 ) ) )
=> ! [X102: term] : ( X92 @ X102 ) ) ) )
=> ! [X104: term > $o,X106: term,X108: subst] :
( ! [X110: term] :
( ( var @ X110 )
=> ( X104 @ ( sub @ X110 @ X108 ) ) )
=> ( ( X104 @ X106 )
=> ! [X112: term] :
( ( var @ X112 )
=> ( X104 @ ( sub @ X112 @ ( push @ X106 @ X108 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ( ! [X4: term,X6: term,X8: subst] :
( ( sub @ ( ap @ X4 @ X6 ) @ X8 )
= ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) )
=> ( ! [X10: term,X12: subst] :
( ( sub @ one @ ( push @ X10 @ X12 ) )
= X10 )
=> ( ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
=> ( ! [X16: term,X18: subst] :
( ( sub @ ( lam @ X16 ) @ X18 )
= ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) )
=> ( ! [X20: term,X22: subst,X24: subst] :
( ( sub @ ( sub @ X20 @ X22 ) @ X24 )
= ( sub @ X20 @ ( comp @ X22 @ X24 ) ) )
=> ( ! [X26: subst] :
( ( comp @ id @ X26 )
= X26 )
=> ( ! [X28: term,X30: subst] :
( ( comp @ sh @ ( push @ X28 @ X30 ) )
= X30 )
=> ( ! [X32: subst,X34: subst,X36: subst] :
( ( comp @ ( comp @ X32 @ X34 ) @ X36 )
= ( comp @ X32 @ ( comp @ X34 @ X36 ) ) )
=> ( ! [X38: term,X40: subst,X42: subst] :
( ( comp @ ( push @ X38 @ X40 ) @ X42 )
= ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) )
=> ( ! [X44: subst] :
( ( comp @ X44 @ id )
= X44 )
=> ( ( ( push @ one @ sh )
= id )
=> ( ! [X46: subst] :
( ( push @ ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) )
= X46 )
=> ( ( var @ one )
=> ( ! [X48: term] :
( ( var @ X48 )
=> ( var @ ( sub @ X48 @ sh ) ) )
=> ( ! [X50: term > $o] :
( ( X50 @ one )
=> ( ! [X52: term] :
( ( var @ X52 )
=> ( ( X50 @ X52 )
=> ( X50 @ ( sub @ X52 @ sh ) ) ) )
=> ! [X54: term] :
( ( var @ X54 )
=> ( X50 @ X54 ) ) ) )
=> ( ! [X56: term,X58: term,X60: term,X62: term] :
( ( ( ap @ X56 @ X60 )
= ( ap @ X58 @ X62 ) )
=> ( X56 = X58 ) )
=> ( ! [X64: term,X66: term,X68: term,X70: term] :
( ( ( ap @ X64 @ X68 )
= ( ap @ X66 @ X70 ) )
=> ( X68 = X70 ) )
=> ( ! [X72: term,X74: term] :
( ( ( lam @ X72 )
= ( lam @ X74 ) )
=> ( X72 = X74 ) )
=> ( ! [X76: term,X78: term] :
( ( ( sub @ X76 @ sh )
= ( sub @ X78 @ sh ) )
=> ( X76 = X78 ) )
=> ( ! [X80: term,X82: term,X84: term] :
( ( lam @ X80 )
!= ( ap @ X82 @ X84 ) )
=> ( ! [X86: term,X88: term] :
~ ( var @ ( ap @ X86 @ X88 ) )
=> ( ! [X90: term] :
~ ( var @ ( lam @ X90 ) )
=> ( ! [X92: term > $o] :
( ! [X94: term] :
( ( var @ X94 )
=> ( X92 @ X94 ) )
=> ( ! [X96: term,X98: term] :
( ( X92 @ X96 )
=> ( ( X92 @ X98 )
=> ( X92 @ ( ap @ X96 @ X98 ) ) ) )
=> ( ! [X100: term] :
( ( X92 @ X100 )
=> ( X92 @ ( lam @ X100 ) ) )
=> ! [X102: term] : ( X92 @ X102 ) ) ) )
=> ! [X104: term > $o,X106: term,X108: subst] :
( ! [X110: term] :
( ( var @ X110 )
=> ( X104 @ ( sub @ X110 @ X108 ) ) )
=> ( ( X104 @ X106 )
=> ! [X112: term] :
( ( var @ X112 )
=> ( X104 @ ( sub @ X112 @ ( push @ X106 @ X108 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( ap @ Y0 @ Y1 ) @ Y2 )
= ( ap @ ( sub @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl2,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl5,plain,
~ ( ( !!
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl9,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( lam @ Y0 ) @ Y1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ Y1 @ sh ) ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl14,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl20,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( ( comp @ id @ Y0 )
= Y0 ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( comp @ Y0 @ Y1 ) @ Y2 )
= ( comp @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl34,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( comp @ ( push @ Y0 @ Y1 ) @ Y2 )
= ( push @ ( sub @ Y0 @ Y2 ) @ ( comp @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl39,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( ( comp @ Y0 @ id )
= Y0 ) )
=> ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl44,plain,
~ ( ( ( push @ one @ sh )
= id )
=> ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl49,plain,
~ ( ( !!
@ ^ [Y0: subst] :
( ( push @ ( sub @ one @ Y0 ) @ ( comp @ sh @ Y0 ) )
= Y0 ) )
=> ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl55,plain,
~ ( ( var @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl59,plain,
~ ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( var @ ( sub @ Y0 @ sh ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl62,plain,
~ ( ( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl65,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y0 = Y1 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl69,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( !!
@ ^ [Y3: term] :
( ( ( ap @ Y0 @ Y2 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y3 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl73,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( lam @ Y0 )
= ( lam @ Y1 ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl78,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( ( ( sub @ Y0 @ sh )
= ( sub @ Y1 @ sh ) )
=> ( Y0 = Y1 ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl84,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( lam @ Y0 )
!= ( ap @ Y1 @ Y2 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl92,plain,
~ ( ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: term] : ( (~) @ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
=> ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl102,plain,
~ ( ( !!
@ ^ [Y0: term] : ( (~) @ ( var @ ( lam @ Y0 ) ) ) )
=> ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl113,plain,
~ ( ( !!
@ ^ [Y0: term > $o] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: term] :
( ( Y0 @ Y1 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( ap @ Y1 @ Y2 ) ) ) ) ) )
=> ( ( !!
@ ^ [Y1: term] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( lam @ Y1 ) ) ) )
=> ( !!
@ ^ [Y1: term] : ( Y0 @ Y1 ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl122,plain,
~ ( !!
@ ^ [Y0: term > $o] :
( !!
@ ^ [Y1: term] :
( !!
@ ^ [Y2: subst] :
( ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ Y2 ) ) ) )
=> ( ( Y0 @ Y1 )
=> ( !!
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl127,plain,
~ ( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( !!
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( '#sk30' @ ( sub @ Y2 @ Y1 ) ) ) )
=> ( ( '#sk30' @ Y0 )
=> ( !!
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( '#sk30' @ ( sub @ Y2 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl129,plain,
~ ( !!
@ ^ [Y0: subst] :
( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( '#sk30' @ ( sub @ Y1 @ Y0 ) ) ) )
=> ( ( '#sk30' @ '#sk39' )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( '#sk30' @ ( sub @ Y1 @ ( push @ '#sk39' @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl131,plain,
~ ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ '#sk49' ) ) ) )
=> ( ( '#sk30' @ '#sk39' )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl135,plain,
~ ( ( '#sk30' @ '#sk39' )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl140,plain,
~ ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl144,plain,
~ ( ( var
@ ( '#sk48'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) )
=> ( '#sk30'
@ ( sub
@ ( '#sk48'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ ( push @ '#sk39' @ '#sk49' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl147,plain,
( var
@ ( '#sk48'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl147_001,plain,
( var
@ ( '#sk48'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl12171,plain,
! [X1: term] :
( ( '#l_lift15327' @ X1 )
= ( '#sk30' @ ( sub @ X1 @ ( push @ '#sk39' @ '#sk49' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12172,plain,
var @ ( '#sk48' @ '#l_lift15327' ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl147,zip_derived_cl12171]) ).
thf(zip_derived_cl148,plain,
~ ( '#sk30'
@ ( sub
@ ( '#sk48'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ ( push @ '#sk39' @ '#sk49' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl12171_002,plain,
! [X1: term] :
( ( '#l_lift15327' @ X1 )
= ( '#sk30' @ ( sub @ X1 @ ( push @ '#sk39' @ '#sk49' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12173,plain,
~ ( '#sk30' @ ( sub @ ( '#sk48' @ '#l_lift15327' ) @ ( push @ '#sk39' @ '#sk49' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl148,zip_derived_cl12171]) ).
thf(zip_derived_cl134,plain,
( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ '#sk49' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl138,plain,
! [X2: term] :
( ( var @ X2 )
=> ( '#sk30' @ ( sub @ X2 @ '#sk49' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl143,plain,
! [X2: term] :
( ~ ( var @ X2 )
| ( '#sk30' @ ( sub @ X2 @ '#sk49' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl138]) ).
thf(zip_derived_cl64,plain,
( !!
@ ^ [Y0: term > $o] :
( ( Y0 @ one )
=> ( ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl67,plain,
! [X2: term > $o] :
( ( X2 @ one )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( X2 @ Y0 )
=> ( X2 @ ( sub @ Y0 @ sh ) ) ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl171,plain,
( ( '#sk30' @ ( sub @ one @ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30' @ ( sub @ ( sub @ Y0 @ sh ) @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl7,plain,
! [X2: term] :
( !!
@ ^ [Y0: subst] :
( ( sub @ one @ ( push @ X2 @ Y0 ) )
= X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl11,plain,
! [X2: term,X4: subst] :
( ( sub @ one @ ( push @ X2 @ X4 ) )
= X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl16,plain,
! [X2: term,X4: subst] :
( ( sub @ one @ ( push @ X2 @ X4 ) )
= X2 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl139,plain,
'#sk30' @ '#sk39',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl205,plain,
( $true
=> ( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30' @ ( sub @ ( sub @ Y0 @ sh ) @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl171,zip_derived_cl16,zip_derived_cl139]) ).
thf(zip_derived_cl206,plain,
( ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30' @ ( sub @ ( sub @ Y0 @ sh ) @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) )
=> ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl207,plain,
( ~ ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30' @ ( sub @ ( sub @ Y0 @ sh ) @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl208,plain,
( ~ ( ( var
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) )
=> ( ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30'
@ ( sub
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ sh )
@ ( push @ '#sk39' @ '#sk49' ) ) ) ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl207]) ).
thf(zip_derived_cl19,plain,
( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( !!
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y0 @ Y1 ) @ Y2 )
= ( sub @ Y0 @ ( comp @ Y1 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl22,plain,
! [X2: term] :
( !!
@ ^ [Y0: subst] :
( !!
@ ^ [Y1: subst] :
( ( sub @ ( sub @ X2 @ Y0 ) @ Y1 )
= ( sub @ X2 @ ( comp @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl26,plain,
! [X2: term,X4: subst] :
( !!
@ ^ [Y0: subst] :
( ( sub @ ( sub @ X2 @ X4 ) @ Y0 )
= ( sub @ X2 @ ( comp @ X4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl30,plain,
! [X2: term,X4: subst,X6: subst] :
( ( sub @ ( sub @ X2 @ X4 ) @ X6 )
= ( sub @ X2 @ ( comp @ X4 @ X6 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl35,plain,
! [X2: term,X4: subst,X6: subst] :
( ( sub @ ( sub @ X2 @ X4 ) @ X6 )
= ( sub @ X2 @ ( comp @ X4 @ X6 ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl28,plain,
( !!
@ ^ [Y0: term] :
( !!
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: term] :
( !!
@ ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X2 @ Y0 ) )
= Y0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl36,plain,
! [X2: term,X4: subst] :
( ( comp @ sh @ ( push @ X2 @ X4 ) )
= X4 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl40,plain,
! [X2: term,X4: subst] :
( ( comp @ sh @ ( push @ X2 @ X4 ) )
= X4 ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl209,plain,
( ~ ( ( var
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) )
=> ( ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ '#sk49' ) ) ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl208,zip_derived_cl35,zip_derived_cl40]) ).
thf(zip_derived_cl211,plain,
( ~ ( ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ ( push @ '#sk39' @ '#sk49' ) ) )
=> ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ '#sk49' ) ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl209]) ).
thf(zip_derived_cl214,plain,
( ~ ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ '#sk49' ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl217,plain,
! [X2: term] :
( ( ( var @ X2 )
=> ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
| ~ ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ '#sk49' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl214]) ).
thf(zip_derived_cl219,plain,
! [X2: term] :
( ~ ( var @ X2 )
| ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) )
| ~ ( '#sk30'
@ ( sub
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
@ '#sk49' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl217]) ).
thf(zip_derived_cl12171_003,plain,
! [X1: term] :
( ( '#l_lift15327' @ X1 )
= ( '#sk30' @ ( sub @ X1 @ ( push @ '#sk39' @ '#sk49' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12176,plain,
! [X2: term] :
( ~ ( var @ X2 )
| ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) )
| ~ ( '#sk30' @ ( sub @ ( '#sk10' @ '#l_lift15327' ) @ '#sk49' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl219,zip_derived_cl12171]) ).
thf(zip_derived_cl210,plain,
( ( var
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) )
| ( !!
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl209]) ).
thf(zip_derived_cl212,plain,
! [X2: term] :
( ( ( var @ X2 )
=> ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) ) )
| ( var
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl215,plain,
! [X2: term] :
( ~ ( var @ X2 )
| ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) )
| ( var
@ ( '#sk10'
@ ^ [Y0: term] : ( '#sk30' @ ( sub @ Y0 @ ( push @ '#sk39' @ '#sk49' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl212]) ).
thf(zip_derived_cl12171_004,plain,
! [X1: term] :
( ( '#l_lift15327' @ X1 )
= ( '#sk30' @ ( sub @ X1 @ ( push @ '#sk39' @ '#sk49' ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl12174,plain,
! [X2: term] :
( ~ ( var @ X2 )
| ( '#sk30' @ ( sub @ X2 @ ( push @ '#sk39' @ '#sk49' ) ) )
| ( var @ ( '#sk10' @ '#l_lift15327' ) ) ),
inference(lambda_lifting,[status(thm)],[zip_derived_cl215,zip_derived_cl12171]) ).
thf(zip_derived_cl12183,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl12172,zip_derived_cl12173,zip_derived_cl143,zip_derived_cl12176,zip_derived_cl12174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ALG251^1 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.O7AbLhuUNj true
% 0.15/0.36 % Computer : n014.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 04:19:01 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.22/0.65 % Total configuration time : 828
% 0.22/0.65 % Estimated wc time : 1656
% 0.22/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 49.01/6.98 % Solved by lams/20_acsne_simpl.sh.
% 49.01/6.98 % done 540 iterations in 6.097s
% 49.01/6.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 49.01/6.98 % SZS output start Refutation
% See solution above
% 49.01/6.99
% 49.01/6.99
% 49.01/6.99 % Terminating...
% 49.70/7.09 % Runner terminated.
% 49.70/7.10 % Zipperpin 1.5 exiting
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