%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN393^4.004 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OPCExQ7cEs true
% Computer : n013.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 : Fri Sep 1 04:03:13 EDT 2023
% Result : Theorem 55.83s 7.91s
% Output : Refutation 55.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 169
% Syntax : Number of formulae : 465 ( 31 unt; 39 typ; 0 def)
% Number of atoms : 12021 ( 30 equ;1493 cnn)
% Maximal formula atoms : 379 ( 28 avg)
% Number of connectives : 28290 (2459 ~;2633 |; 735 &;15803 @)
% ( 0 <=>;3470 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 39 usr; 15 con; 0-3 aty)
% (3190 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 3903 (3250 ^; 653 !; 0 ?;3903 :)
% Comments :
%------------------------------------------------------------------------------
thf('#form24_type',type,
'#form24': $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(a3_type,type,
a3: $i > $o ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf('#sk10_type',type,
'#sk10': $i > $i ).
thf(a2_type,type,
a2: $i > $o ).
thf(irel_type,type,
irel: $i > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk22_type',type,
'#sk22': $i > $i ).
thf('#form3_type',type,
'#form3': $o ).
thf('#form19_type',type,
'#form19': $i > $o ).
thf('#sk13_type',type,
'#sk13': $i ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf('#sk12_type',type,
'#sk12': $i > $i ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a1_type,type,
a1: $i > $o ).
thf('#form11_type',type,
'#form11': $o ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form8_type',type,
'#form8': $i > $o ).
thf('#sk23_type',type,
'#sk23': $i > $i ).
thf('#form14_type',type,
'#form14': $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(a4_type,type,
a4: $i > $o ).
thf('#form17_type',type,
'#form17': $i > $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf('#sk7_type',type,
'#sk7': $i ).
thf('#form5_type',type,
'#form5': $o ).
thf('#sk16_type',type,
'#sk16': $i > $i ).
thf('#sk18_type',type,
'#sk18': $i > $i ).
thf(iequiv_type,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk21_type',type,
'#sk21': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#sk15_type',type,
'#sk15': $i > $i ).
thf('#form20_type',type,
'#form20': $i > $o ).
thf(ivalid,axiom,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[ivalid]) ).
thf('1',plain,
( ivalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(iequiv,axiom,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ) ).
thf('2',plain,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('3',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( irel @ V_2 @ X4 )
=> ( V_1 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('5',plain,
( mor
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).
thf('9',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iimplies,'3','9']) ).
thf('11',plain,
( iimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(iand,axiom,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
thf(mand,axiom,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ) ).
thf('12',plain,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
& ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
inference(simplify_rw_rule,[status(thm)],[iand,'13']) ).
thf('15',plain,
( iand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('16',plain,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iequiv,'11','15','3','9','13','5','7']) ).
thf('17',plain,
( iequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( iand @ ( iimplies @ V_1 @ V_2 ) @ ( iimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('18',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('19',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(con,conjecture,
ivalid @ ( iequiv @ ( iequiv @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a3 ) ) @ ( iatom @ a4 ) ) @ ( iequiv @ ( iatom @ a4 ) @ ( iequiv @ ( iatom @ a3 ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( ! [X180: $i] :
( ( irel @ X4 @ X180 )
=> ( ( ! [X212: $i] :
( ( irel @ X180 @ X212 )
=> ( ( ! [X228: $i] :
( ( irel @ X212 @ X228 )
=> ( ( ! [X236: $i] :
( ( irel @ X228 @ X236 )
=> ( a1 @ X236 ) )
| ~ ! [X234: $i] :
( ( irel @ X228 @ X234 )
=> ( a2 @ X234 ) ) )
& ( ! [X232: $i] :
( ( irel @ X228 @ X232 )
=> ( a2 @ X232 ) )
| ~ ! [X230: $i] :
( ( irel @ X228 @ X230 )
=> ( a1 @ X230 ) ) ) ) )
| ~ ! [X226: $i] :
( ( irel @ X212 @ X226 )
=> ( a3 @ X226 ) ) )
& ( ! [X224: $i] :
( ( irel @ X212 @ X224 )
=> ( a3 @ X224 ) )
| ~ ! [X214: $i] :
( ( irel @ X212 @ X214 )
=> ( ( ! [X222: $i] :
( ( irel @ X214 @ X222 )
=> ( a1 @ X222 ) )
| ~ ! [X220: $i] :
( ( irel @ X214 @ X220 )
=> ( a2 @ X220 ) ) )
& ( ! [X218: $i] :
( ( irel @ X214 @ X218 )
=> ( a2 @ X218 ) )
| ~ ! [X216: $i] :
( ( irel @ X214 @ X216 )
=> ( a1 @ X216 ) ) ) ) ) ) ) )
| ~ ! [X210: $i] :
( ( irel @ X180 @ X210 )
=> ( a4 @ X210 ) ) )
& ( ! [X208: $i] :
( ( irel @ X180 @ X208 )
=> ( a4 @ X208 ) )
| ~ ! [X182: $i] :
( ( irel @ X180 @ X182 )
=> ( ( ! [X198: $i] :
( ( irel @ X182 @ X198 )
=> ( ( ! [X206: $i] :
( ( irel @ X198 @ X206 )
=> ( a1 @ X206 ) )
| ~ ! [X204: $i] :
( ( irel @ X198 @ X204 )
=> ( a2 @ X204 ) ) )
& ( ! [X202: $i] :
( ( irel @ X198 @ X202 )
=> ( a2 @ X202 ) )
| ~ ! [X200: $i] :
( ( irel @ X198 @ X200 )
=> ( a1 @ X200 ) ) ) ) )
| ~ ! [X196: $i] :
( ( irel @ X182 @ X196 )
=> ( a3 @ X196 ) ) )
& ( ! [X194: $i] :
( ( irel @ X182 @ X194 )
=> ( a3 @ X194 ) )
| ~ ! [X184: $i] :
( ( irel @ X182 @ X184 )
=> ( ( ! [X192: $i] :
( ( irel @ X184 @ X192 )
=> ( a1 @ X192 ) )
| ~ ! [X190: $i] :
( ( irel @ X184 @ X190 )
=> ( a2 @ X190 ) ) )
& ( ! [X188: $i] :
( ( irel @ X184 @ X188 )
=> ( a2 @ X188 ) )
| ~ ! [X186: $i] :
( ( irel @ X184 @ X186 )
=> ( a1 @ X186 ) ) ) ) ) ) ) ) ) ) )
| ~ ! [X122: $i] :
( ( irel @ X4 @ X122 )
=> ( ( ! [X178: $i] :
( ( irel @ X122 @ X178 )
=> ( a4 @ X178 ) )
| ~ ! [X152: $i] :
( ( irel @ X122 @ X152 )
=> ( ( ! [X176: $i] :
( ( irel @ X152 @ X176 )
=> ( a3 @ X176 ) )
| ~ ! [X166: $i] :
( ( irel @ X152 @ X166 )
=> ( ( ! [X174: $i] :
( ( irel @ X166 @ X174 )
=> ( a2 @ X174 ) )
| ~ ! [X172: $i] :
( ( irel @ X166 @ X172 )
=> ( a1 @ X172 ) ) )
& ( ! [X170: $i] :
( ( irel @ X166 @ X170 )
=> ( a1 @ X170 ) )
| ~ ! [X168: $i] :
( ( irel @ X166 @ X168 )
=> ( a2 @ X168 ) ) ) ) ) )
& ( ! [X156: $i] :
( ( irel @ X152 @ X156 )
=> ( ( ! [X164: $i] :
( ( irel @ X156 @ X164 )
=> ( a2 @ X164 ) )
| ~ ! [X162: $i] :
( ( irel @ X156 @ X162 )
=> ( a1 @ X162 ) ) )
& ( ! [X160: $i] :
( ( irel @ X156 @ X160 )
=> ( a1 @ X160 ) )
| ~ ! [X158: $i] :
( ( irel @ X156 @ X158 )
=> ( a2 @ X158 ) ) ) ) )
| ~ ! [X154: $i] :
( ( irel @ X152 @ X154 )
=> ( a3 @ X154 ) ) ) ) ) )
& ( ! [X126: $i] :
( ( irel @ X122 @ X126 )
=> ( ( ! [X150: $i] :
( ( irel @ X126 @ X150 )
=> ( a3 @ X150 ) )
| ~ ! [X140: $i] :
( ( irel @ X126 @ X140 )
=> ( ( ! [X148: $i] :
( ( irel @ X140 @ X148 )
=> ( a2 @ X148 ) )
| ~ ! [X146: $i] :
( ( irel @ X140 @ X146 )
=> ( a1 @ X146 ) ) )
& ( ! [X144: $i] :
( ( irel @ X140 @ X144 )
=> ( a1 @ X144 ) )
| ~ ! [X142: $i] :
( ( irel @ X140 @ X142 )
=> ( a2 @ X142 ) ) ) ) ) )
& ( ! [X130: $i] :
( ( irel @ X126 @ X130 )
=> ( ( ! [X138: $i] :
( ( irel @ X130 @ X138 )
=> ( a2 @ X138 ) )
| ~ ! [X136: $i] :
( ( irel @ X130 @ X136 )
=> ( a1 @ X136 ) ) )
& ( ! [X134: $i] :
( ( irel @ X130 @ X134 )
=> ( a1 @ X134 ) )
| ~ ! [X132: $i] :
( ( irel @ X130 @ X132 )
=> ( a2 @ X132 ) ) ) ) )
| ~ ! [X128: $i] :
( ( irel @ X126 @ X128 )
=> ( a3 @ X128 ) ) ) ) )
| ~ ! [X124: $i] :
( ( irel @ X122 @ X124 )
=> ( a4 @ X124 ) ) ) ) ) )
& ( ! [X64: $i] :
( ( irel @ X4 @ X64 )
=> ( ( ! [X120: $i] :
( ( irel @ X64 @ X120 )
=> ( a4 @ X120 ) )
| ~ ! [X94: $i] :
( ( irel @ X64 @ X94 )
=> ( ( ! [X118: $i] :
( ( irel @ X94 @ X118 )
=> ( a3 @ X118 ) )
| ~ ! [X108: $i] :
( ( irel @ X94 @ X108 )
=> ( ( ! [X116: $i] :
( ( irel @ X108 @ X116 )
=> ( a2 @ X116 ) )
| ~ ! [X114: $i] :
( ( irel @ X108 @ X114 )
=> ( a1 @ X114 ) ) )
& ( ! [X112: $i] :
( ( irel @ X108 @ X112 )
=> ( a1 @ X112 ) )
| ~ ! [X110: $i] :
( ( irel @ X108 @ X110 )
=> ( a2 @ X110 ) ) ) ) ) )
& ( ! [X98: $i] :
( ( irel @ X94 @ X98 )
=> ( ( ! [X106: $i] :
( ( irel @ X98 @ X106 )
=> ( a2 @ X106 ) )
| ~ ! [X104: $i] :
( ( irel @ X98 @ X104 )
=> ( a1 @ X104 ) ) )
& ( ! [X102: $i] :
( ( irel @ X98 @ X102 )
=> ( a1 @ X102 ) )
| ~ ! [X100: $i] :
( ( irel @ X98 @ X100 )
=> ( a2 @ X100 ) ) ) ) )
| ~ ! [X96: $i] :
( ( irel @ X94 @ X96 )
=> ( a3 @ X96 ) ) ) ) ) )
& ( ! [X68: $i] :
( ( irel @ X64 @ X68 )
=> ( ( ! [X92: $i] :
( ( irel @ X68 @ X92 )
=> ( a3 @ X92 ) )
| ~ ! [X82: $i] :
( ( irel @ X68 @ X82 )
=> ( ( ! [X90: $i] :
( ( irel @ X82 @ X90 )
=> ( a2 @ X90 ) )
| ~ ! [X88: $i] :
( ( irel @ X82 @ X88 )
=> ( a1 @ X88 ) ) )
& ( ! [X86: $i] :
( ( irel @ X82 @ X86 )
=> ( a1 @ X86 ) )
| ~ ! [X84: $i] :
( ( irel @ X82 @ X84 )
=> ( a2 @ X84 ) ) ) ) ) )
& ( ! [X72: $i] :
( ( irel @ X68 @ X72 )
=> ( ( ! [X80: $i] :
( ( irel @ X72 @ X80 )
=> ( a2 @ X80 ) )
| ~ ! [X78: $i] :
( ( irel @ X72 @ X78 )
=> ( a1 @ X78 ) ) )
& ( ! [X76: $i] :
( ( irel @ X72 @ X76 )
=> ( a1 @ X76 ) )
| ~ ! [X74: $i] :
( ( irel @ X72 @ X74 )
=> ( a2 @ X74 ) ) ) ) )
| ~ ! [X70: $i] :
( ( irel @ X68 @ X70 )
=> ( a3 @ X70 ) ) ) ) )
| ~ ! [X66: $i] :
( ( irel @ X64 @ X66 )
=> ( a4 @ X66 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X38: $i] :
( ( irel @ X6 @ X38 )
=> ( ( ! [X54: $i] :
( ( irel @ X38 @ X54 )
=> ( ( ! [X62: $i] :
( ( irel @ X54 @ X62 )
=> ( a1 @ X62 ) )
| ~ ! [X60: $i] :
( ( irel @ X54 @ X60 )
=> ( a2 @ X60 ) ) )
& ( ! [X58: $i] :
( ( irel @ X54 @ X58 )
=> ( a2 @ X58 ) )
| ~ ! [X56: $i] :
( ( irel @ X54 @ X56 )
=> ( a1 @ X56 ) ) ) ) )
| ~ ! [X52: $i] :
( ( irel @ X38 @ X52 )
=> ( a3 @ X52 ) ) )
& ( ! [X50: $i] :
( ( irel @ X38 @ X50 )
=> ( a3 @ X50 ) )
| ~ ! [X40: $i] :
( ( irel @ X38 @ X40 )
=> ( ( ! [X48: $i] :
( ( irel @ X40 @ X48 )
=> ( a1 @ X48 ) )
| ~ ! [X46: $i] :
( ( irel @ X40 @ X46 )
=> ( a2 @ X46 ) ) )
& ( ! [X44: $i] :
( ( irel @ X40 @ X44 )
=> ( a2 @ X44 ) )
| ~ ! [X42: $i] :
( ( irel @ X40 @ X42 )
=> ( a1 @ X42 ) ) ) ) ) ) ) )
| ~ ! [X36: $i] :
( ( irel @ X6 @ X36 )
=> ( a4 @ X36 ) ) )
& ( ! [X34: $i] :
( ( irel @ X6 @ X34 )
=> ( a4 @ X34 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( ( ! [X24: $i] :
( ( irel @ X8 @ X24 )
=> ( ( ! [X32: $i] :
( ( irel @ X24 @ X32 )
=> ( a1 @ X32 ) )
| ~ ! [X30: $i] :
( ( irel @ X24 @ X30 )
=> ( a2 @ X30 ) ) )
& ( ! [X28: $i] :
( ( irel @ X24 @ X28 )
=> ( a2 @ X28 ) )
| ~ ! [X26: $i] :
( ( irel @ X24 @ X26 )
=> ( a1 @ X26 ) ) ) ) )
| ~ ! [X22: $i] :
( ( irel @ X8 @ X22 )
=> ( a3 @ X22 ) ) )
& ( ! [X20: $i] :
( ( irel @ X8 @ X20 )
=> ( a3 @ X20 ) )
| ~ ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ( ! [X18: $i] :
( ( irel @ X10 @ X18 )
=> ( a1 @ X18 ) )
| ~ ! [X16: $i] :
( ( irel @ X10 @ X16 )
=> ( a2 @ X16 ) ) )
& ( ! [X14: $i] :
( ( irel @ X10 @ X14 )
=> ( a2 @ X14 ) )
| ~ ! [X12: $i] :
( ( irel @ X10 @ X12 )
=> ( a1 @ X12 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( ! [X180: $i] :
( ( irel @ X4 @ X180 )
=> ( ( ! [X212: $i] :
( ( irel @ X180 @ X212 )
=> ( ( ! [X228: $i] :
( ( irel @ X212 @ X228 )
=> ( ( ! [X236: $i] :
( ( irel @ X228 @ X236 )
=> ( a1 @ X236 ) )
| ~ ! [X234: $i] :
( ( irel @ X228 @ X234 )
=> ( a2 @ X234 ) ) )
& ( ! [X232: $i] :
( ( irel @ X228 @ X232 )
=> ( a2 @ X232 ) )
| ~ ! [X230: $i] :
( ( irel @ X228 @ X230 )
=> ( a1 @ X230 ) ) ) ) )
| ~ ! [X226: $i] :
( ( irel @ X212 @ X226 )
=> ( a3 @ X226 ) ) )
& ( ! [X224: $i] :
( ( irel @ X212 @ X224 )
=> ( a3 @ X224 ) )
| ~ ! [X214: $i] :
( ( irel @ X212 @ X214 )
=> ( ( ! [X222: $i] :
( ( irel @ X214 @ X222 )
=> ( a1 @ X222 ) )
| ~ ! [X220: $i] :
( ( irel @ X214 @ X220 )
=> ( a2 @ X220 ) ) )
& ( ! [X218: $i] :
( ( irel @ X214 @ X218 )
=> ( a2 @ X218 ) )
| ~ ! [X216: $i] :
( ( irel @ X214 @ X216 )
=> ( a1 @ X216 ) ) ) ) ) ) ) )
| ~ ! [X210: $i] :
( ( irel @ X180 @ X210 )
=> ( a4 @ X210 ) ) )
& ( ! [X208: $i] :
( ( irel @ X180 @ X208 )
=> ( a4 @ X208 ) )
| ~ ! [X182: $i] :
( ( irel @ X180 @ X182 )
=> ( ( ! [X198: $i] :
( ( irel @ X182 @ X198 )
=> ( ( ! [X206: $i] :
( ( irel @ X198 @ X206 )
=> ( a1 @ X206 ) )
| ~ ! [X204: $i] :
( ( irel @ X198 @ X204 )
=> ( a2 @ X204 ) ) )
& ( ! [X202: $i] :
( ( irel @ X198 @ X202 )
=> ( a2 @ X202 ) )
| ~ ! [X200: $i] :
( ( irel @ X198 @ X200 )
=> ( a1 @ X200 ) ) ) ) )
| ~ ! [X196: $i] :
( ( irel @ X182 @ X196 )
=> ( a3 @ X196 ) ) )
& ( ! [X194: $i] :
( ( irel @ X182 @ X194 )
=> ( a3 @ X194 ) )
| ~ ! [X184: $i] :
( ( irel @ X182 @ X184 )
=> ( ( ! [X192: $i] :
( ( irel @ X184 @ X192 )
=> ( a1 @ X192 ) )
| ~ ! [X190: $i] :
( ( irel @ X184 @ X190 )
=> ( a2 @ X190 ) ) )
& ( ! [X188: $i] :
( ( irel @ X184 @ X188 )
=> ( a2 @ X188 ) )
| ~ ! [X186: $i] :
( ( irel @ X184 @ X186 )
=> ( a1 @ X186 ) ) ) ) ) ) ) ) ) ) )
| ~ ! [X122: $i] :
( ( irel @ X4 @ X122 )
=> ( ( ! [X178: $i] :
( ( irel @ X122 @ X178 )
=> ( a4 @ X178 ) )
| ~ ! [X152: $i] :
( ( irel @ X122 @ X152 )
=> ( ( ! [X176: $i] :
( ( irel @ X152 @ X176 )
=> ( a3 @ X176 ) )
| ~ ! [X166: $i] :
( ( irel @ X152 @ X166 )
=> ( ( ! [X174: $i] :
( ( irel @ X166 @ X174 )
=> ( a2 @ X174 ) )
| ~ ! [X172: $i] :
( ( irel @ X166 @ X172 )
=> ( a1 @ X172 ) ) )
& ( ! [X170: $i] :
( ( irel @ X166 @ X170 )
=> ( a1 @ X170 ) )
| ~ ! [X168: $i] :
( ( irel @ X166 @ X168 )
=> ( a2 @ X168 ) ) ) ) ) )
& ( ! [X156: $i] :
( ( irel @ X152 @ X156 )
=> ( ( ! [X164: $i] :
( ( irel @ X156 @ X164 )
=> ( a2 @ X164 ) )
| ~ ! [X162: $i] :
( ( irel @ X156 @ X162 )
=> ( a1 @ X162 ) ) )
& ( ! [X160: $i] :
( ( irel @ X156 @ X160 )
=> ( a1 @ X160 ) )
| ~ ! [X158: $i] :
( ( irel @ X156 @ X158 )
=> ( a2 @ X158 ) ) ) ) )
| ~ ! [X154: $i] :
( ( irel @ X152 @ X154 )
=> ( a3 @ X154 ) ) ) ) ) )
& ( ! [X126: $i] :
( ( irel @ X122 @ X126 )
=> ( ( ! [X150: $i] :
( ( irel @ X126 @ X150 )
=> ( a3 @ X150 ) )
| ~ ! [X140: $i] :
( ( irel @ X126 @ X140 )
=> ( ( ! [X148: $i] :
( ( irel @ X140 @ X148 )
=> ( a2 @ X148 ) )
| ~ ! [X146: $i] :
( ( irel @ X140 @ X146 )
=> ( a1 @ X146 ) ) )
& ( ! [X144: $i] :
( ( irel @ X140 @ X144 )
=> ( a1 @ X144 ) )
| ~ ! [X142: $i] :
( ( irel @ X140 @ X142 )
=> ( a2 @ X142 ) ) ) ) ) )
& ( ! [X130: $i] :
( ( irel @ X126 @ X130 )
=> ( ( ! [X138: $i] :
( ( irel @ X130 @ X138 )
=> ( a2 @ X138 ) )
| ~ ! [X136: $i] :
( ( irel @ X130 @ X136 )
=> ( a1 @ X136 ) ) )
& ( ! [X134: $i] :
( ( irel @ X130 @ X134 )
=> ( a1 @ X134 ) )
| ~ ! [X132: $i] :
( ( irel @ X130 @ X132 )
=> ( a2 @ X132 ) ) ) ) )
| ~ ! [X128: $i] :
( ( irel @ X126 @ X128 )
=> ( a3 @ X128 ) ) ) ) )
| ~ ! [X124: $i] :
( ( irel @ X122 @ X124 )
=> ( a4 @ X124 ) ) ) ) ) )
& ( ! [X64: $i] :
( ( irel @ X4 @ X64 )
=> ( ( ! [X120: $i] :
( ( irel @ X64 @ X120 )
=> ( a4 @ X120 ) )
| ~ ! [X94: $i] :
( ( irel @ X64 @ X94 )
=> ( ( ! [X118: $i] :
( ( irel @ X94 @ X118 )
=> ( a3 @ X118 ) )
| ~ ! [X108: $i] :
( ( irel @ X94 @ X108 )
=> ( ( ! [X116: $i] :
( ( irel @ X108 @ X116 )
=> ( a2 @ X116 ) )
| ~ ! [X114: $i] :
( ( irel @ X108 @ X114 )
=> ( a1 @ X114 ) ) )
& ( ! [X112: $i] :
( ( irel @ X108 @ X112 )
=> ( a1 @ X112 ) )
| ~ ! [X110: $i] :
( ( irel @ X108 @ X110 )
=> ( a2 @ X110 ) ) ) ) ) )
& ( ! [X98: $i] :
( ( irel @ X94 @ X98 )
=> ( ( ! [X106: $i] :
( ( irel @ X98 @ X106 )
=> ( a2 @ X106 ) )
| ~ ! [X104: $i] :
( ( irel @ X98 @ X104 )
=> ( a1 @ X104 ) ) )
& ( ! [X102: $i] :
( ( irel @ X98 @ X102 )
=> ( a1 @ X102 ) )
| ~ ! [X100: $i] :
( ( irel @ X98 @ X100 )
=> ( a2 @ X100 ) ) ) ) )
| ~ ! [X96: $i] :
( ( irel @ X94 @ X96 )
=> ( a3 @ X96 ) ) ) ) ) )
& ( ! [X68: $i] :
( ( irel @ X64 @ X68 )
=> ( ( ! [X92: $i] :
( ( irel @ X68 @ X92 )
=> ( a3 @ X92 ) )
| ~ ! [X82: $i] :
( ( irel @ X68 @ X82 )
=> ( ( ! [X90: $i] :
( ( irel @ X82 @ X90 )
=> ( a2 @ X90 ) )
| ~ ! [X88: $i] :
( ( irel @ X82 @ X88 )
=> ( a1 @ X88 ) ) )
& ( ! [X86: $i] :
( ( irel @ X82 @ X86 )
=> ( a1 @ X86 ) )
| ~ ! [X84: $i] :
( ( irel @ X82 @ X84 )
=> ( a2 @ X84 ) ) ) ) ) )
& ( ! [X72: $i] :
( ( irel @ X68 @ X72 )
=> ( ( ! [X80: $i] :
( ( irel @ X72 @ X80 )
=> ( a2 @ X80 ) )
| ~ ! [X78: $i] :
( ( irel @ X72 @ X78 )
=> ( a1 @ X78 ) ) )
& ( ! [X76: $i] :
( ( irel @ X72 @ X76 )
=> ( a1 @ X76 ) )
| ~ ! [X74: $i] :
( ( irel @ X72 @ X74 )
=> ( a2 @ X74 ) ) ) ) )
| ~ ! [X70: $i] :
( ( irel @ X68 @ X70 )
=> ( a3 @ X70 ) ) ) ) )
| ~ ! [X66: $i] :
( ( irel @ X64 @ X66 )
=> ( a4 @ X66 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X38: $i] :
( ( irel @ X6 @ X38 )
=> ( ( ! [X54: $i] :
( ( irel @ X38 @ X54 )
=> ( ( ! [X62: $i] :
( ( irel @ X54 @ X62 )
=> ( a1 @ X62 ) )
| ~ ! [X60: $i] :
( ( irel @ X54 @ X60 )
=> ( a2 @ X60 ) ) )
& ( ! [X58: $i] :
( ( irel @ X54 @ X58 )
=> ( a2 @ X58 ) )
| ~ ! [X56: $i] :
( ( irel @ X54 @ X56 )
=> ( a1 @ X56 ) ) ) ) )
| ~ ! [X52: $i] :
( ( irel @ X38 @ X52 )
=> ( a3 @ X52 ) ) )
& ( ! [X50: $i] :
( ( irel @ X38 @ X50 )
=> ( a3 @ X50 ) )
| ~ ! [X40: $i] :
( ( irel @ X38 @ X40 )
=> ( ( ! [X48: $i] :
( ( irel @ X40 @ X48 )
=> ( a1 @ X48 ) )
| ~ ! [X46: $i] :
( ( irel @ X40 @ X46 )
=> ( a2 @ X46 ) ) )
& ( ! [X44: $i] :
( ( irel @ X40 @ X44 )
=> ( a2 @ X44 ) )
| ~ ! [X42: $i] :
( ( irel @ X40 @ X42 )
=> ( a1 @ X42 ) ) ) ) ) ) ) )
| ~ ! [X36: $i] :
( ( irel @ X6 @ X36 )
=> ( a4 @ X36 ) ) )
& ( ! [X34: $i] :
( ( irel @ X6 @ X34 )
=> ( a4 @ X34 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( ( ! [X24: $i] :
( ( irel @ X8 @ X24 )
=> ( ( ! [X32: $i] :
( ( irel @ X24 @ X32 )
=> ( a1 @ X32 ) )
| ~ ! [X30: $i] :
( ( irel @ X24 @ X30 )
=> ( a2 @ X30 ) ) )
& ( ! [X28: $i] :
( ( irel @ X24 @ X28 )
=> ( a2 @ X28 ) )
| ~ ! [X26: $i] :
( ( irel @ X24 @ X26 )
=> ( a1 @ X26 ) ) ) ) )
| ~ ! [X22: $i] :
( ( irel @ X8 @ X22 )
=> ( a3 @ X22 ) ) )
& ( ! [X20: $i] :
( ( irel @ X8 @ X20 )
=> ( a3 @ X20 ) )
| ~ ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( ( ! [X18: $i] :
( ( irel @ X10 @ X18 )
=> ( a1 @ X18 ) )
| ~ ! [X16: $i] :
( ( irel @ X10 @ X16 )
=> ( a2 @ X16 ) ) )
& ( ! [X14: $i] :
( ( irel @ X10 @ X14 )
=> ( a2 @ X14 ) )
| ~ ! [X12: $i] :
( ( irel @ X10 @ X12 )
=> ( a1 @ X12 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a4 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) ) ) )
& ( ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a2 @ Y4 ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( a1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl20,zip_derived_cl24]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl46_001,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl60,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( ( irel @ X2 @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl60]) ).
thf(zip_derived_cl74,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl104,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl104_002,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl123,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl125,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form14' @ X4 )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl104,zip_derived_cl123]) ).
thf(zip_derived_cl148,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( '#form14' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl182,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ ( '#form14' @ X4 )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl148]) ).
thf(zip_derived_cl203,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( '#form14' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl182]) ).
thf(zip_derived_cl224,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl225,plain,
! [X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( '#form20' @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl224]) ).
thf(zip_derived_cl256,plain,
! [X6: $i,X8: $i] :
( ( ( irel @ X6 @ X8 )
=> ( a1 @ X8 ) )
| ~ ( '#form20' @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl225]) ).
thf(zip_derived_cl272,plain,
! [X6: $i,X8: $i] :
( ~ ( irel @ X6 @ X8 )
| ( a1 @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( '#form20' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl256]) ).
thf(zip_derived_cl286,plain,
! [X6: $i,X8: $i] :
( ~ ( ( irel @ X6 @ ( '#sk22' @ X6 ) )
=> ( a2 @ ( '#sk22' @ X6 ) ) )
| ~ ( '#form20' @ X6 )
| ( a1 @ X8 )
| ~ ( irel @ X6 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl272]) ).
thf(zip_derived_cl293,plain,
! [X6: $i,X8: $i] :
( ~ ( a2 @ ( '#sk22' @ X6 ) )
| ~ ( irel @ X6 @ X8 )
| ( a1 @ X8 )
| ~ ( '#form20' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl286]) ).
thf(zip_derived_cl3,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl5,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
( ~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl13,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl12,plain,
( ( irel @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl18,plain,
( ~ '#form3'
| ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl13,zip_derived_cl15]) ).
thf(zip_derived_cl23,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl29,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl37,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( irel @ '#sk2' @ '#sk6' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl55,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl15_003,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl16,plain,
( ~ ( ( irel @ '#sk1' @ '#sk4' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl28,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl50,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl51,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl52,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ( ( irel @ '#sk4' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_004,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl69,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl55,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl83,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl69]) ).
thf(zip_derived_cl95,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl108,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl109,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl108]) ).
thf(zip_derived_cl110,plain,
( ~ ( ( irel @ '#sk6' @ '#sk13' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl53_005,plain,
! [X2: $i] :
( ( ( irel @ '#sk4' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl65_006,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_007,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl67,plain,
! [X2: $i] :
( ( '#form8' @ '#sk4' )
| '#form3'
| ( ( irel @ '#sk4' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl53,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ~ ( irel @ '#sk4' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| '#form3'
| ( '#form8' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl93,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl106,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl128,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_008,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl132,plain,
( ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( ( irel @ '#sk6' @ '#sk13' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl110,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl162,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl188,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl162]) ).
thf(zip_derived_cl210,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl236,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl210]) ).
thf(zip_derived_cl237,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl236]) ).
thf(zip_derived_cl238,plain,
( ~ ( ( irel @ '#sk13' @ '#sk21' )
=> ( a1 @ '#sk21' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl237]) ).
thf(zip_derived_cl264,plain,
( ~ ( a1 @ '#sk21' )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl238]) ).
thf(zip_derived_cl263,plain,
( ( irel @ '#sk13' @ '#sk21' )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl238]) ).
thf(zip_derived_cl277,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl280,plain,
( ~ '#form24'
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( a1 @ '#sk21' ) ),
inference(renaming,[status(thm)],[zip_derived_cl264,zip_derived_cl277]) ).
thf(zip_derived_cl292,plain,
! [X6: $i,X8: $i] :
( ( irel @ X6 @ ( '#sk22' @ X6 ) )
| ~ ( irel @ X6 @ X8 )
| ( a1 @ X8 )
| ~ ( '#form20' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl286]) ).
thf(zip_derived_cl277_009,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl278,plain,
( ~ ( ( irel @ '#sk13' @ ( '#sk22' @ '#sk13' ) )
=> ( a2 @ ( '#sk22' @ '#sk13' ) ) )
| '#form24' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl277]) ).
thf(zip_derived_cl287,plain,
( ( irel @ '#sk13' @ ( '#sk22' @ '#sk13' ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl202,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( '#form14' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl182]) ).
thf(zip_derived_cl221,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl222,plain,
! [X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( '#form19' @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl221]) ).
thf(zip_derived_cl255,plain,
! [X6: $i,X8: $i] :
( ( ( irel @ X6 @ X8 )
=> ( a2 @ X8 ) )
| ~ ( '#form19' @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl222]) ).
thf(zip_derived_cl271,plain,
! [X6: $i,X8: $i] :
( ~ ( irel @ X6 @ X8 )
| ( a2 @ X8 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( '#form19' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl255]) ).
thf(zip_derived_cl285,plain,
! [X6: $i,X8: $i] :
( ~ ( ( irel @ X6 @ ( '#sk23' @ X6 ) )
=> ( a1 @ ( '#sk23' @ X6 ) ) )
| ~ ( '#form19' @ X6 )
| ( a2 @ X8 )
| ~ ( irel @ X6 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl271]) ).
thf(zip_derived_cl290,plain,
! [X6: $i,X8: $i] :
( ( irel @ X6 @ ( '#sk23' @ X6 ) )
| ~ ( irel @ X6 @ X8 )
| ( a2 @ X8 )
| ~ ( '#form19' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl285]) ).
thf(zip_derived_cl1804,plain,
( '#form24'
| ~ ( '#form19' @ '#sk13' )
| ( a2 @ ( '#sk22' @ '#sk13' ) )
| ( irel @ '#sk13' @ ( '#sk23' @ '#sk13' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl287,zip_derived_cl290]) ).
thf(zip_derived_cl288,plain,
( ~ ( a2 @ ( '#sk22' @ '#sk13' ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl2183,plain,
( ( irel @ '#sk13' @ ( '#sk23' @ '#sk13' ) )
| ~ ( '#form19' @ '#sk13' )
| '#form24' ),
inference(clc,[status(thm)],[zip_derived_cl1804,zip_derived_cl288]) ).
thf(zip_derived_cl287_010,plain,
( ( irel @ '#sk13' @ ( '#sk22' @ '#sk13' ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl263_011,plain,
( ( irel @ '#sk13' @ '#sk21' )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl238]) ).
thf(zip_derived_cl277_012,plain,
( '#form24'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl279,plain,
( ~ '#form24'
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( irel @ '#sk13' @ '#sk21' ) ),
inference(renaming,[status(thm)],[zip_derived_cl263,zip_derived_cl277]) ).
thf(zip_derived_cl288_013,plain,
( ~ ( a2 @ ( '#sk22' @ '#sk13' ) )
| '#form24' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl278]) ).
thf(zip_derived_cl291,plain,
! [X6: $i,X8: $i] :
( ~ ( a1 @ ( '#sk23' @ X6 ) )
| ~ ( irel @ X6 @ X8 )
| ( a2 @ X8 )
| ~ ( '#form19' @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl285]) ).
thf(zip_derived_cl161,plain,
( ( irel @ '#sk6' @ '#sk13' )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl211,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl239,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl240,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl241,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl240]) ).
thf(zip_derived_cl242,plain,
! [X2: $i] :
( ( ( irel @ '#sk13' @ X2 )
=> ( a2 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl241]) ).
thf(zip_derived_cl265,plain,
! [X2: $i] :
( ~ ( irel @ '#sk13' @ X2 )
| ( a2 @ X2 )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk13' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl242]) ).
thf(zip_derived_cl281,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ '#sk13' @ X4 )
=> ( a1 @ X4 ) )
| ~ ( '#form14' @ '#sk6' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( a2 @ X2 )
| ~ ( irel @ '#sk13' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl289,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk13' @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk13' @ X2 )
| ( a2 @ X2 )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form14' @ '#sk6' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl281]) ).
thf(zip_derived_cl96,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl111,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl112,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl113,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl114,plain,
! [X2: $i] :
( ( ( irel @ '#sk6' @ X2 )
=> ( a3 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl133,plain,
! [X2: $i] :
( ~ ( irel @ '#sk6' @ X2 )
| ( a3 @ X2 )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk6' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl163,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ '#sk6' @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ( a3 @ X2 )
| ~ ( irel @ '#sk6' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl189,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk6' @ X4 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ ( irel @ '#sk6' @ X2 )
| ( a3 @ X2 )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl163]) ).
thf(zip_derived_cl213,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ( a3 @ X2 )
| ~ ( irel @ '#sk6' @ X2 )
| ~ ( irel @ '#sk6' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl106_014,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl128_015,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_016,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl130,plain,
! [X2: $i] :
( ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl106,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl158,plain,
! [X2: $i] :
( ~ ( ( irel @ X2 @ ( '#sk16' @ X2 ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ( '#form14' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl130]) ).
thf(zip_derived_cl186,plain,
! [X2: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl207,plain,
! [X2: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ( '#form14' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl230,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_017,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl244,plain,
! [X2: $i,X4: $i] :
( ( '#form19' @ X4 )
| ~ ( irel @ '#sk6' @ X4 )
| ~ ( irel @ '#sk6' @ X2 )
| ( a3 @ X2 )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(renaming,[status(thm)],[zip_derived_cl213,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl212,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ( a3 @ X2 )
| ~ ( irel @ '#sk6' @ X2 )
| ~ ( irel @ '#sk6' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl224_018,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl243,plain,
! [X2: $i,X4: $i] :
( ( '#form20' @ X4 )
| ~ ( irel @ '#sk6' @ X4 )
| ~ ( irel @ '#sk6' @ X2 )
| ( a3 @ X2 )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(renaming,[status(thm)],[zip_derived_cl212,zip_derived_cl224]) ).
thf(zip_derived_cl54,plain,
( ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl65_019,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_020,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl68,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( irel @ '#sk2' @ '#sk6' ) ),
inference(renaming,[status(thm)],[zip_derived_cl54,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl12_021,plain,
( ( irel @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15_022,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl17,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl30,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl39,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ '#form3'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl40,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ '#form3'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( ( irel @ '#sk2' @ X2 )
=> ( a4 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X2: $i] :
( ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ '#sk2' @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk2' @ X4 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl115,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl128_023,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_024,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl134,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form14' @ X4 )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl115,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl134_025,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form14' @ X4 )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl115,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl164,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl166,plain,
! [X2: $i,X4: $i] :
( ( '#form17' @ X4 )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3'
| ~ ( '#form14' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl134,zip_derived_cl164]) ).
thf(zip_derived_cl98,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl116,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl128_026,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_027,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl135,plain,
! [X2: $i,X4: $i] :
( ( '#form14' @ X4 )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl116,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl135_028,plain,
! [X2: $i,X4: $i] :
( ( '#form14' @ X4 )
| ~ '#form3'
| ( a4 @ X2 )
| ~ ( irel @ '#sk2' @ X2 )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl116,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl167,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl164_029,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl169,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form17' @ X4 )
| ~ ( irel @ '#sk2' @ X4 )
| ~ ( irel @ '#sk2' @ X2 )
| ( a4 @ X2 )
| ~ '#form3'
| ( '#form14' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl135,zip_derived_cl167,zip_derived_cl164]) ).
thf(zip_derived_cl19_030,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24_031,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl19,zip_derived_cl24]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a4 @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk10' @ X2 ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl99,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl118,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl139,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl118]) ).
thf(zip_derived_cl140,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl141,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl128_032,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_033,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl142,plain,
! [X2: $i,X4: $i] :
( ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl141,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl171,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ ( '#sk10' @ X2 ) @ X6 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( '#form14' @ ( '#sk10' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl142]) ).
thf(zip_derived_cl195,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ ( '#sk10' @ X2 ) @ X6 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl218,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( '#form14' @ ( '#sk10' @ X2 ) )
| ~ ( irel @ ( '#sk10' @ X2 ) @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl195]) ).
thf(zip_derived_cl230_034,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_035,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl252,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( '#form19' @ X6 )
| ~ ( irel @ ( '#sk10' @ X2 ) @ X6 )
| ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl218,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl219,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( '#form14' @ ( '#sk10' @ X2 ) )
| ~ ( irel @ ( '#sk10' @ X2 ) @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl195]) ).
thf(zip_derived_cl167_036,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl168,plain,
! [X4: $i] :
( ~ ( ( irel @ X4 @ ( '#sk18' @ X4 ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ( '#form17' @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl167]) ).
thf(zip_derived_cl192,plain,
! [X4: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ( '#form17' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl168]) ).
thf(zip_derived_cl216,plain,
! [X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( '#form17' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl192]) ).
thf(zip_derived_cl247,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_037,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl253,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( '#form20' @ X6 )
| ~ ( irel @ ( '#sk10' @ X2 ) @ X6 )
| ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl219,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl117,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl136,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl117]) ).
thf(zip_derived_cl137,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl128_038,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_039,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl138,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form14' @ ( '#sk10' @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl137,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl170,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk10' @ X2 ) @ ( '#sk16' @ ( '#sk10' @ X2 ) ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( '#form14' @ ( '#sk10' @ X2 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl138]) ).
thf(zip_derived_cl194,plain,
! [X2: $i,X4: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl217,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( '#form14' @ ( '#sk10' @ X2 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl194]) ).
thf(zip_derived_cl230_040,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_041,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl251,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form19' @ ( '#sk16' @ ( '#sk10' @ X2 ) ) )
| ~ ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ X2 ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl217,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl247_042,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_043,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl269,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form20' @ ( '#sk16' @ ( '#sk10' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( '#form14' @ ( '#sk10' @ X2 ) )
| ~ ( '#form19' @ ( '#sk16' @ ( '#sk10' @ X2 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl251,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl60_044,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ~ ( ( irel @ X2 @ ( '#sk9' @ X2 ) )
=> ( a4 @ ( '#sk9' @ X2 ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl75,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl128_045,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl129,plain,
! [X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( a3 @ X6 ) )
| ~ ( '#form14' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl159,plain,
! [X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( a3 @ X6 )
| ~ ( '#form14' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl202_046,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( '#form14' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl182]) ).
thf(zip_derived_cl221_047,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl223,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( '#form19' @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( '#form14' @ X4 )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl202,zip_derived_cl221]) ).
thf(zip_derived_cl203_048,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( '#form14' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl182]) ).
thf(zip_derived_cl224_049,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl226,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( '#form20' @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( '#form14' @ X4 )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl203,zip_derived_cl224]) ).
thf(zip_derived_cl76,plain,
! [X2: $i] :
( ~ ( a4 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl193,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk10' @ X2 ) @ ( '#sk16' @ ( '#sk10' @ X2 ) ) )
| ~ ( '#form14' @ ( '#sk10' @ X2 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a4 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl34,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl47,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl48,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a4 @ Y0 ) ) )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
( ~ ( ( irel @ '#sk4' @ '#sk7' )
=> ( a4 @ '#sk7' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl64,plain,
( ~ ( a4 @ '#sk7' )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl63,plain,
( ( irel @ '#sk4' @ '#sk7' )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl77,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl80,plain,
( ~ '#form11'
| '#form3'
| ~ ( a4 @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl64,zip_derived_cl77]) ).
thf(zip_derived_cl123_050,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl124,plain,
! [X4: $i] :
( ~ ( ( irel @ X4 @ ( '#sk15' @ X4 ) )
=> ( a3 @ ( '#sk15' @ X4 ) ) )
| ( '#form14' @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl149,plain,
! [X4: $i] :
( ( irel @ X4 @ ( '#sk15' @ X4 ) )
| ( '#form14' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl21,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl150,plain,
! [X4: $i] :
( ~ ( a3 @ ( '#sk15' @ X4 ) )
| ( '#form14' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl124]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl103,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl122,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( a3 @ X6 ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl147,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( a3 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl181,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X4 @ ( '#sk16' @ X4 ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X6 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl201,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ ( irel @ X4 @ X6 )
| ( a3 @ X6 )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl181]) ).
thf(zip_derived_cl220,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X6 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl201]) ).
thf(zip_derived_cl230_051,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_052,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl254,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#form19' @ ( '#sk16' @ X4 ) )
| ~ ( irel @ X4 @ X6 )
| ( a3 @ X6 )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl220,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl247_053,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_054,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl270,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( '#form20' @ ( '#sk16' @ X4 ) )
| ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( '#form19' @ ( '#sk16' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl254,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl63_055,plain,
( ( irel @ '#sk4' @ '#sk7' )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl77_056,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl79,plain,
( ~ '#form11'
| '#form3'
| ( irel @ '#sk4' @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl63,zip_derived_cl77]) ).
thf(zip_derived_cl24_057,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a4 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) ) ) )
& ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form5' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl65_058,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_059,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl59,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl88,plain,
! [X2: $i] :
( ~ ( ( irel @ X2 @ ( '#sk12' @ X2 ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl101,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl65_060,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a4 @ X4 ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk10' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a4 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl102,plain,
! [X2: $i] :
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl121,plain,
! [X2: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl146,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl177,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl178,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl177]) ).
thf(zip_derived_cl179,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl178]) ).
thf(zip_derived_cl128_061,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_062,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl180,plain,
! [X2: $i] :
( ( '#form14' @ ( '#sk12' @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl179,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl167_063,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl164_064,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl199,plain,
! [X2: $i] :
( ( '#form17' @ ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( '#form14' @ ( '#sk12' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl180,zip_derived_cl167,zip_derived_cl164]) ).
thf(zip_derived_cl145,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl121]) ).
thf(zip_derived_cl174,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl175,plain,
! [X2: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl174]) ).
thf(zip_derived_cl167_065,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl164_066,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl176,plain,
! [X2: $i] :
( ~ ( '#form17' @ ( '#sk12' @ X2 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk12' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl175,zip_derived_cl167,zip_derived_cl164]) ).
thf(zip_derived_cl128_067,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_068,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl198,plain,
! [X2: $i] :
( ~ ( '#form14' @ ( '#sk12' @ X2 ) )
| ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form17' @ ( '#sk12' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl176,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl200,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( irel @ X4 @ ( '#sk16' @ X4 ) )
| ~ ( irel @ X4 @ X6 )
| ( a3 @ X6 )
| ~ ( irel @ X2 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl181]) ).
thf(zip_derived_cl77_069,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl78,plain,
( ~ ( ( irel @ '#sk4' @ ( '#sk10' @ '#sk4' ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ) )
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl91,plain,
( ( irel @ '#sk4' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl92,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) )
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl105,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
| '#form11' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl126,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| '#form11'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl151,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| '#form11'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl152,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl128_070,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_071,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl153,plain,
( ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl152,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl183,plain,
( ~ ( ( irel @ ( '#sk10' @ '#sk4' ) @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| '#form11'
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl153]) ).
thf(zip_derived_cl205,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl183]) ).
thf(zip_derived_cl227,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| '#form11'
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl230_072,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_073,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl257,plain,
( ~ ( '#form19' @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) )
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl227,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl247_074,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_075,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl273,plain,
( ~ ( '#form20' @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) )
| '#form11'
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| ~ ( '#form19' @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl257,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl94,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl107,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl128_076,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_077,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl131,plain,
! [X2: $i] :
( ~ ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl107,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl160,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ~ ( '#form14' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl187,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ~ ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl160]) ).
thf(zip_derived_cl208,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ~ ( '#form14' @ X2 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl187]) ).
thf(zip_derived_cl230_078,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_079,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl234,plain,
! [X2: $i,X4: $i] :
( ( '#form19' @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl208,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl209,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ~ ( '#form14' @ X2 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl187]) ).
thf(zip_derived_cl224_080,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl235,plain,
! [X2: $i,X4: $i] :
( ( '#form20' @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl209,zip_derived_cl224]) ).
thf(zip_derived_cl185,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk16' @ X2 ) )
| ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl58,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl65_081,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_082,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl58,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl100,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl119,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( '#form8' @ X2 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl143,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl119]) ).
thf(zip_derived_cl167_083,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl164_084,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl172,plain,
! [X2: $i,X4: $i] :
( ( '#form17' @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( '#form8' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl143,zip_derived_cl167,zip_derived_cl164]) ).
thf(zip_derived_cl128_085,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_086,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl196,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form14' @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( '#form17' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl172,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl204,plain,
( ( irel @ ( '#sk10' @ '#sk4' ) @ ( '#sk16' @ ( '#sk10' @ '#sk4' ) ) )
| ~ ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl183]) ).
thf(zip_derived_cl207_087,plain,
! [X2: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ( '#form14' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl186]) ).
thf(zip_derived_cl230_088,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_089,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl233,plain,
! [X2: $i] :
( ~ ( '#form19' @ ( '#sk16' @ X2 ) )
| ( '#form14' @ X2 )
| ( '#form8' @ '#sk4' )
| '#form3'
| ~ ( irel @ '#sk4' @ X2 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk16' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl207,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl247_090,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_091,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl260,plain,
! [X2: $i] :
( ~ ( '#form20' @ ( '#sk16' @ X2 ) )
| ~ ( irel @ '#sk4' @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' )
| ( '#form14' @ X2 )
| ~ ( '#form19' @ ( '#sk16' @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl233,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl191,plain,
! [X4: $i] :
( ( irel @ X4 @ ( '#sk18' @ X4 ) )
| ( '#form17' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl168]) ).
thf(zip_derived_cl120,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( '#form8' @ X2 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl144,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl120]) ).
thf(zip_derived_cl128_092,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_093,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl173,plain,
! [X2: $i,X4: $i] :
( ( '#form14' @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( '#form8' @ X2 )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl144,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl167_094,plain,
! [X4: $i] :
( ( '#form17' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl164_095,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl197,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form17' @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( '#form14' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl173,zip_derived_cl167,zip_derived_cl164]) ).
thf(zip_derived_cl164_096,plain,
! [X4: $i] :
( ~ ( '#form17' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl165,plain,
! [X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ ( '#form17' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl164]) ).
thf(zip_derived_cl190,plain,
! [X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ ( '#form17' @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl215,plain,
! [X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ ( '#form17' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl190]) ).
thf(zip_derived_cl230_097,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_098,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl246,plain,
! [X4: $i,X6: $i] :
( ( '#form19' @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( '#form17' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl215,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl214,plain,
! [X4: $i,X6: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ ( '#form17' @ X4 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl190]) ).
thf(zip_derived_cl224_099,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl245,plain,
! [X4: $i,X6: $i] :
( ( '#form20' @ X6 )
| ~ ( irel @ X4 @ X6 )
| ~ ( '#form17' @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl214,zip_derived_cl224]) ).
thf(zip_derived_cl127,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form11'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl154,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form11'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl127]) ).
thf(zip_derived_cl155,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form11'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl154]) ).
thf(zip_derived_cl156,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| '#form11'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl155]) ).
thf(zip_derived_cl128_100,plain,
! [X4: $i] :
( ~ ( '#form14' @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl123_101,plain,
! [X4: $i] :
( ( '#form14' @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( a3 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl157,plain,
( ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk10' @ '#sk4' ) @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl156,zip_derived_cl128,zip_derived_cl123]) ).
thf(zip_derived_cl184,plain,
! [X2: $i] :
( ( ( irel @ ( '#sk10' @ '#sk4' ) @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| '#form11'
| ( '#form14' @ ( '#sk10' @ '#sk4' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl157]) ).
thf(zip_derived_cl206,plain,
! [X2: $i] :
( ~ ( irel @ ( '#sk10' @ '#sk4' ) @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl184]) ).
thf(zip_derived_cl228,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| '#form11'
| ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| ~ ( irel @ ( '#sk10' @ '#sk4' ) @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl230_102,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_103,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl258,plain,
! [X2: $i] :
( ( '#form19' @ X2 )
| ~ ( irel @ ( '#sk10' @ '#sk4' ) @ X2 )
| ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl228,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl229,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| '#form11'
| ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| ~ ( irel @ ( '#sk10' @ '#sk4' ) @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl206]) ).
thf(zip_derived_cl247_104,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_105,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl259,plain,
! [X2: $i] :
( ( '#form20' @ X2 )
| ~ ( irel @ ( '#sk10' @ '#sk4' ) @ X2 )
| ( '#form14' @ ( '#sk10' @ '#sk4' ) )
| '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl229,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl216_106,plain,
! [X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ( '#form17' @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl192]) ).
thf(zip_derived_cl247_107,plain,
! [X6: $i] :
( ( '#form20' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl224_108,plain,
! [X6: $i] :
( ~ ( '#form20' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl250,plain,
! [X4: $i] :
( ~ ( '#form20' @ ( '#sk18' @ X4 ) )
| ( '#form17' @ X4 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk18' @ X4 ) @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl216,zip_derived_cl247,zip_derived_cl224]) ).
thf(zip_derived_cl230_109,plain,
! [X6: $i] :
( ( '#form19' @ X6 )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221_110,plain,
! [X6: $i] :
( ~ ( '#form19' @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X6 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl266,plain,
! [X4: $i] :
( ~ ( '#form19' @ ( '#sk18' @ X4 ) )
| ( '#form17' @ X4 )
| ~ ( '#form20' @ ( '#sk18' @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl250,zip_derived_cl230,zip_derived_cl221]) ).
thf(zip_derived_cl18539,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl293,zip_derived_cl280,zip_derived_cl292,zip_derived_cl2183,zip_derived_cl287,zip_derived_cl279,zip_derived_cl288,zip_derived_cl291,zip_derived_cl161,zip_derived_cl289,zip_derived_cl244,zip_derived_cl243,zip_derived_cl68,zip_derived_cl17,zip_derived_cl166,zip_derived_cl169,zip_derived_cl252,zip_derived_cl253,zip_derived_cl269,zip_derived_cl75,zip_derived_cl159,zip_derived_cl223,zip_derived_cl226,zip_derived_cl76,zip_derived_cl193,zip_derived_cl80,zip_derived_cl149,zip_derived_cl21,zip_derived_cl150,zip_derived_cl270,zip_derived_cl79,zip_derived_cl101,zip_derived_cl82,zip_derived_cl85,zip_derived_cl199,zip_derived_cl198,zip_derived_cl200,zip_derived_cl91,zip_derived_cl273,zip_derived_cl234,zip_derived_cl235,zip_derived_cl185,zip_derived_cl196,zip_derived_cl204,zip_derived_cl260,zip_derived_cl191,zip_derived_cl197,zip_derived_cl246,zip_derived_cl245,zip_derived_cl258,zip_derived_cl259,zip_derived_cl266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYN393^4.004 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.OPCExQ7cEs true
% 0.13/0.36 % Computer : n013.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 21:40:32 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Running portfolio for 300 s
% 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.36 % Number of cores: 8
% 0.13/0.36 % Python version: Python 3.6.8
% 0.13/0.36 % Running in HO mode
% 0.22/0.69 % Total configuration time : 828
% 0.22/0.69 % Estimated wc time : 1656
% 0.22/0.69 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.77 % /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
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.80 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.82 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 55.83/7.91 % Solved by lams/20_acsne_simpl.sh.
% 55.83/7.91 % done 5427 iterations in 6.657s
% 55.83/7.91 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 55.83/7.91 % SZS output start Refutation
% See solution above
% 55.83/7.96
% 55.83/7.96
% 55.83/7.96 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 55.83/7.96 % Terminating...
% 55.94/8.08 % Runner terminated.
% 55.94/8.09 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------