TSTP Solution File: SYO069^4.003 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO069^4.003 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.PCqlrOOSHP true
% Computer : n009.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 05:49:34 EDT 2023
% Result : Theorem 25.94s 3.90s
% Output : Refutation 25.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 59
% Syntax : Number of formulae : 299 ( 83 unt; 31 typ; 0 def)
% Number of atoms : 3451 ( 27 equ; 352 cnn)
% Maximal formula atoms : 131 ( 12 avg)
% Number of connectives : 8377 ( 835 ~; 913 |; 145 &;4839 @)
% ( 0 <=>; 879 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 98 ( 98 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 31 usr; 7 con; 0-3 aty)
% ( 766 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1189 ( 820 ^; 369 !; 0 ?;1189 :)
% Comments :
%------------------------------------------------------------------------------
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf('#sk10_type',type,
'#sk10': $i > $i ).
thf(a2_type,type,
a2: $i > $o ).
thf('#sk11_type',type,
'#sk11': $i > $i ).
thf('#sk5_type',type,
'#sk5': $i > $i ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf(a1_type,type,
a1: $i > $o ).
thf('#sk6_type',type,
'#sk6': $i > $i ).
thf(irel_type,type,
irel: $i > $i > $o ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#form3_type',type,
'#form3': $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(b0_type,type,
b0: $i > $o ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a0_type,type,
a0: $i > $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(b2_type,type,
b2: $i > $o ).
thf(f_type,type,
f: $i > $o ).
thf(b1_type,type,
b1: $i > $o ).
thf('#sk4_type',type,
'#sk4': $i > $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(b3_type,type,
b3: $i > $o ).
thf('#sk7_type',type,
'#sk7': $i > $i ).
thf(a3_type,type,
a3: $i > $o ).
thf('#sk8_type',type,
'#sk8': $i > $i ).
thf('#sk12_type',type,
'#sk12': $i > $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $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(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(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('16',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('17',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(con,conjecture,
ivalid @ ( iand @ ( iimplies @ ( iand @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ b0 ) ) @ ( iatom @ a3 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) ) ) ) ) @ ( iatom @ f ) ) @ ( iimplies @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b2 ) @ ( iatom @ a3 ) ) @ ( iatom @ a2 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b1 ) @ ( iatom @ a2 ) ) @ ( iatom @ a1 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b0 ) @ ( iatom @ a1 ) ) @ ( iatom @ a0 ) ) @ ( iand @ ( iimplies @ ( iimplies @ ( iatom @ b3 ) @ ( iatom @ b0 ) ) @ ( iatom @ a3 ) ) @ ( iimplies @ ( iatom @ a0 ) @ ( iatom @ f ) ) ) ) ) ) @ ( iatom @ f ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( ! [X84: $i] :
( ( irel @ X4 @ X84 )
=> ( f @ X84 ) )
| ~ ! [X46: $i] :
( ( irel @ X4 @ X46 )
=> ( ( ! [X82: $i] :
( ( irel @ X46 @ X82 )
=> ( f @ X82 ) )
| ~ ! [X80: $i] :
( ( irel @ X46 @ X80 )
=> ( a0 @ X80 ) ) )
& ( ! [X78: $i] :
( ( irel @ X46 @ X78 )
=> ( a3 @ X78 ) )
| ~ ! [X72: $i] :
( ( irel @ X46 @ X72 )
=> ( ! [X76: $i] :
( ( irel @ X72 @ X76 )
=> ( b0 @ X76 ) )
| ~ ! [X74: $i] :
( ( irel @ X72 @ X74 )
=> ( b3 @ X74 ) ) ) ) )
& ( ! [X70: $i] :
( ( irel @ X46 @ X70 )
=> ( a0 @ X70 ) )
| ~ ! [X64: $i] :
( ( irel @ X46 @ X64 )
=> ( ! [X68: $i] :
( ( irel @ X64 @ X68 )
=> ( a1 @ X68 ) )
| ~ ! [X66: $i] :
( ( irel @ X64 @ X66 )
=> ( b0 @ X66 ) ) ) ) )
& ( ! [X62: $i] :
( ( irel @ X46 @ X62 )
=> ( a1 @ X62 ) )
| ~ ! [X56: $i] :
( ( irel @ X46 @ X56 )
=> ( ! [X60: $i] :
( ( irel @ X56 @ X60 )
=> ( a2 @ X60 ) )
| ~ ! [X58: $i] :
( ( irel @ X56 @ X58 )
=> ( b1 @ X58 ) ) ) ) )
& ( ! [X54: $i] :
( ( irel @ X46 @ X54 )
=> ( a2 @ X54 ) )
| ~ ! [X48: $i] :
( ( irel @ X46 @ X48 )
=> ( ! [X52: $i] :
( ( irel @ X48 @ X52 )
=> ( a3 @ X52 ) )
| ~ ! [X50: $i] :
( ( irel @ X48 @ X50 )
=> ( b2 @ X50 ) ) ) ) ) ) ) )
& ( ! [X44: $i] :
( ( irel @ X4 @ X44 )
=> ( f @ X44 ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X42: $i] :
( ( irel @ X6 @ X42 )
=> ( a2 @ X42 ) )
| ~ ! [X36: $i] :
( ( irel @ X6 @ X36 )
=> ( ! [X40: $i] :
( ( irel @ X36 @ X40 )
=> ( a3 @ X40 ) )
| ~ ! [X38: $i] :
( ( irel @ X36 @ X38 )
=> ( b2 @ X38 ) ) ) ) )
& ( ! [X34: $i] :
( ( irel @ X6 @ X34 )
=> ( a1 @ X34 ) )
| ~ ! [X28: $i] :
( ( irel @ X6 @ X28 )
=> ( ! [X32: $i] :
( ( irel @ X28 @ X32 )
=> ( a2 @ X32 ) )
| ~ ! [X30: $i] :
( ( irel @ X28 @ X30 )
=> ( b1 @ X30 ) ) ) ) )
& ( ! [X26: $i] :
( ( irel @ X6 @ X26 )
=> ( a0 @ X26 ) )
| ~ ! [X20: $i] :
( ( irel @ X6 @ X20 )
=> ( ! [X24: $i] :
( ( irel @ X20 @ X24 )
=> ( a1 @ X24 ) )
| ~ ! [X22: $i] :
( ( irel @ X20 @ X22 )
=> ( b0 @ X22 ) ) ) ) )
& ( ! [X18: $i] :
( ( irel @ X6 @ X18 )
=> ( a3 @ X18 ) )
| ~ ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( b0 @ X16 ) )
| ~ ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( b3 @ X14 ) ) ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( f @ X10 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( a0 @ X8 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( ! [X84: $i] :
( ( irel @ X4 @ X84 )
=> ( f @ X84 ) )
| ~ ! [X46: $i] :
( ( irel @ X4 @ X46 )
=> ( ( ! [X82: $i] :
( ( irel @ X46 @ X82 )
=> ( f @ X82 ) )
| ~ ! [X80: $i] :
( ( irel @ X46 @ X80 )
=> ( a0 @ X80 ) ) )
& ( ! [X78: $i] :
( ( irel @ X46 @ X78 )
=> ( a3 @ X78 ) )
| ~ ! [X72: $i] :
( ( irel @ X46 @ X72 )
=> ( ! [X76: $i] :
( ( irel @ X72 @ X76 )
=> ( b0 @ X76 ) )
| ~ ! [X74: $i] :
( ( irel @ X72 @ X74 )
=> ( b3 @ X74 ) ) ) ) )
& ( ! [X70: $i] :
( ( irel @ X46 @ X70 )
=> ( a0 @ X70 ) )
| ~ ! [X64: $i] :
( ( irel @ X46 @ X64 )
=> ( ! [X68: $i] :
( ( irel @ X64 @ X68 )
=> ( a1 @ X68 ) )
| ~ ! [X66: $i] :
( ( irel @ X64 @ X66 )
=> ( b0 @ X66 ) ) ) ) )
& ( ! [X62: $i] :
( ( irel @ X46 @ X62 )
=> ( a1 @ X62 ) )
| ~ ! [X56: $i] :
( ( irel @ X46 @ X56 )
=> ( ! [X60: $i] :
( ( irel @ X56 @ X60 )
=> ( a2 @ X60 ) )
| ~ ! [X58: $i] :
( ( irel @ X56 @ X58 )
=> ( b1 @ X58 ) ) ) ) )
& ( ! [X54: $i] :
( ( irel @ X46 @ X54 )
=> ( a2 @ X54 ) )
| ~ ! [X48: $i] :
( ( irel @ X46 @ X48 )
=> ( ! [X52: $i] :
( ( irel @ X48 @ X52 )
=> ( a3 @ X52 ) )
| ~ ! [X50: $i] :
( ( irel @ X48 @ X50 )
=> ( b2 @ X50 ) ) ) ) ) ) ) )
& ( ! [X44: $i] :
( ( irel @ X4 @ X44 )
=> ( f @ X44 ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X42: $i] :
( ( irel @ X6 @ X42 )
=> ( a2 @ X42 ) )
| ~ ! [X36: $i] :
( ( irel @ X6 @ X36 )
=> ( ! [X40: $i] :
( ( irel @ X36 @ X40 )
=> ( a3 @ X40 ) )
| ~ ! [X38: $i] :
( ( irel @ X36 @ X38 )
=> ( b2 @ X38 ) ) ) ) )
& ( ! [X34: $i] :
( ( irel @ X6 @ X34 )
=> ( a1 @ X34 ) )
| ~ ! [X28: $i] :
( ( irel @ X6 @ X28 )
=> ( ! [X32: $i] :
( ( irel @ X28 @ X32 )
=> ( a2 @ X32 ) )
| ~ ! [X30: $i] :
( ( irel @ X28 @ X30 )
=> ( b1 @ X30 ) ) ) ) )
& ( ! [X26: $i] :
( ( irel @ X6 @ X26 )
=> ( a0 @ X26 ) )
| ~ ! [X20: $i] :
( ( irel @ X6 @ X20 )
=> ( ! [X24: $i] :
( ( irel @ X20 @ X24 )
=> ( a1 @ X24 ) )
| ~ ! [X22: $i] :
( ( irel @ X20 @ X22 )
=> ( b0 @ X22 ) ) ) ) )
& ( ! [X18: $i] :
( ( irel @ X6 @ X18 )
=> ( a3 @ X18 ) )
| ~ ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( b0 @ X16 ) )
| ~ ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( b3 @ X14 ) ) ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( f @ X10 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( a0 @ X8 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl2,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a3 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b2 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a2 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b1 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( a1 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b0 @ Y3 ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( b3 @ Y3 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( f @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl9,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl10,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl13,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ~ ( $true
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl14,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( f @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl17,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl12,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl27,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl35,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl74,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( f @ X4 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl100,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk4' @ X2 ) )
=> ( a0 @ ( '#sk4' @ X2 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( f @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl117,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk4' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl20_001,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25_002,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl20,zip_derived_cl25]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( f @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( f @ X4 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk4' @ X2 ) )
=> ( a0 @ ( '#sk4' @ X2 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( f @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl68,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk4' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl170,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( f @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ ( '#sk4' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl117,zip_derived_cl68]) ).
thf(zip_derived_cl533,plain,
( ( irel @ '#sk1' @ ( '#sk4' @ '#sk1' ) )
| ( f @ '#sk2' )
| ~ ( irel @ '#sk1' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl170]) ).
thf(zip_derived_cl18,plain,
~ ( f @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(refl_axiom,axiom,
! [X: $i] : ( irel @ X @ X ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[refl_axiom]) ).
thf(zip_derived_cl3,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl547,plain,
irel @ '#sk1' @ ( '#sk4' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl18,zip_derived_cl3]) ).
thf(trans_axiom,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( ( irel @ Y @ Z )
& ( irel @ X @ Y ) )
=> ( irel @ X @ Z ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( irel @ Y1 @ Y2 )
& ( irel @ Y0 @ Y1 ) )
=> ( irel @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[trans_axiom]) ).
thf(zip_derived_cl4,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( irel @ Y0 @ Y1 )
& ( irel @ X2 @ Y0 ) )
=> ( irel @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( irel @ X4 @ Y0 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl567,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk4' @ '#sk1' ) )
| ~ ( irel @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl547,zip_derived_cl8]) ).
thf(zip_derived_cl547_003,plain,
irel @ '#sk1' @ ( '#sk4' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl18,zip_derived_cl3]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl72,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a0 @ X4 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl98,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk6' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl114,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl135,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl143,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) )
=> ( a1 @ ( '#sk10' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl153,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl22,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25_004,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl30,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl22,zip_derived_cl25]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a0 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a0 @ X4 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk6' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl103,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) )
=> ( a1 @ ( '#sk10' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl122,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl177,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ( irel @ ( '#sk6' @ X2 ) @ ( '#sk10' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl153,zip_derived_cl122]) ).
thf(zip_derived_cl1082,plain,
( ( irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk10' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ '#sk1' )
| ( a0 @ ( '#sk4' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl547,zip_derived_cl177]) ).
thf(zip_derived_cl3_005,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl17_006,plain,
irel @ '#sk1' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl3_007,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl118,plain,
! [X2: $i,X4: $i] :
( ~ ( a0 @ ( '#sk4' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl69,plain,
! [X2: $i,X4: $i] :
( ~ ( a0 @ ( '#sk4' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( f @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl161,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( f @ X4 )
| ~ ( irel @ X2 @ X4 )
| ~ ( a0 @ ( '#sk4' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl118,zip_derived_cl69]) ).
thf(zip_derived_cl192,plain,
! [X0: $i] :
( ~ ( a0 @ ( '#sk4' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ X0 )
| ( f @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl3,zip_derived_cl161]) ).
thf(zip_derived_cl209,plain,
( ( f @ '#sk2' )
| ~ ( a0 @ ( '#sk4' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl192]) ).
thf(zip_derived_cl18_008,plain,
~ ( f @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl215,plain,
~ ( a0 @ ( '#sk4' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl209,zip_derived_cl18]) ).
thf(zip_derived_cl1108,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk10' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl1082,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl50,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl60,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk7' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl111,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk7' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25_009,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl23,zip_derived_cl25]) ).
thf(zip_derived_cl38,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b1 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk7' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) ) ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl79,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk7' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl167,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ ( '#sk7' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl111,zip_derived_cl79]) ).
thf(zip_derived_cl1129,plain,
( ( irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk7' @ ( '#sk6' @ '#sk1' ) ) )
| ( a1 @ ( '#sk10' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1108,zip_derived_cl167]) ).
thf(zip_derived_cl547_010,plain,
irel @ '#sk1' @ ( '#sk4' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl18,zip_derived_cl3]) ).
thf(zip_derived_cl154,plain,
! [X2: $i,X4: $i] :
( ~ ( a1 @ ( '#sk10' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl123,plain,
! [X2: $i,X4: $i] :
( ~ ( a1 @ ( '#sk10' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl164,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( a1 @ ( '#sk10' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl154,zip_derived_cl123]) ).
thf(zip_derived_cl564,plain,
( ~ ( a1 @ ( '#sk10' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ '#sk1' )
| ( a0 @ ( '#sk4' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl547,zip_derived_cl164]) ).
thf(zip_derived_cl3_011,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl215_012,plain,
~ ( a0 @ ( '#sk4' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl209,zip_derived_cl18]) ).
thf(zip_derived_cl595,plain,
~ ( a1 @ ( '#sk10' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl564,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl547_013,plain,
irel @ '#sk1' @ ( '#sk4' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl533,zip_derived_cl18,zip_derived_cl3]) ).
thf(zip_derived_cl113,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk6' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl98]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk6' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl168,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ ( '#sk6' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl113,zip_derived_cl77]) ).
thf(zip_derived_cl560,plain,
( ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a0 @ ( '#sk4' @ '#sk1' ) )
| ~ ( irel @ '#sk1' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl547,zip_derived_cl168]) ).
thf(zip_derived_cl215_014,plain,
~ ( a0 @ ( '#sk4' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl209,zip_derived_cl18]) ).
thf(zip_derived_cl3_015,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl591,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl1150,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk7' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl1129,zip_derived_cl595,zip_derived_cl591]) ).
thf(zip_derived_cl1108_016,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk10' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl1082,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl112,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl97]) ).
thf(zip_derived_cl133,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl141,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk7' @ X2 ) @ ( '#sk11' @ X2 ) )
=> ( a2 @ ( '#sk11' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl150,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ ( '#sk11' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl80,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( b1 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl92,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl105,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk7' @ X2 ) @ ( '#sk11' @ X2 ) )
=> ( a2 @ ( '#sk11' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl125,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk7' @ X2 ) @ ( '#sk11' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl176,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ( irel @ ( '#sk7' @ X2 ) @ ( '#sk11' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl150,zip_derived_cl125]) ).
thf(zip_derived_cl1124,plain,
( ( irel @ ( '#sk7' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a1 @ ( '#sk10' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1108,zip_derived_cl176]) ).
thf(zip_derived_cl591_017,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl595_018,plain,
~ ( a1 @ ( '#sk10' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl564,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl1145,plain,
irel @ ( '#sk7' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl1124,zip_derived_cl591,zip_derived_cl595]) ).
thf(zip_derived_cl8_019,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl1272,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ X0 @ ( '#sk7' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1145,zip_derived_cl8]) ).
thf(zip_derived_cl15378,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1150,zip_derived_cl1272]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk8' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl109,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl24,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25_020,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl24,zip_derived_cl25]) ).
thf(zip_derived_cl39,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b2 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk8' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) ) ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl81,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk8' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl166,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ ( '#sk8' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl109,zip_derived_cl81]) ).
thf(zip_derived_cl15406,plain,
( ( irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk8' @ ( '#sk6' @ '#sk1' ) ) )
| ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl15378,zip_derived_cl166]) ).
thf(zip_derived_cl1108_021,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk10' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl1082,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl151,plain,
! [X2: $i,X4: $i] :
( ~ ( a2 @ ( '#sk11' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl126,plain,
! [X2: $i,X4: $i] :
( ~ ( a2 @ ( '#sk11' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a1 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl105]) ).
thf(zip_derived_cl163,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( a2 @ ( '#sk11' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl151,zip_derived_cl126]) ).
thf(zip_derived_cl1133,plain,
( ~ ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a1 @ ( '#sk10' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1108,zip_derived_cl163]) ).
thf(zip_derived_cl591_022,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl595_023,plain,
~ ( a1 @ ( '#sk10' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl564,zip_derived_cl3,zip_derived_cl215]) ).
thf(zip_derived_cl1154,plain,
~ ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1133,zip_derived_cl591,zip_derived_cl595]) ).
thf(zip_derived_cl591_024,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl15431,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk8' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl15406,zip_derived_cl1154,zip_derived_cl591]) ).
thf(zip_derived_cl15378_025,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1150,zip_derived_cl1272]) ).
thf(zip_derived_cl110,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl131,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl139,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk8' @ X2 ) @ ( '#sk12' @ X2 ) )
=> ( a3 @ ( '#sk12' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl147,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ ( '#sk12' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( b2 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl94,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl107,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk8' @ X2 ) @ ( '#sk12' @ X2 ) )
=> ( a3 @ ( '#sk12' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl128,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk8' @ X2 ) @ ( '#sk12' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl175,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ( irel @ ( '#sk8' @ X2 ) @ ( '#sk12' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl147,zip_derived_cl128]) ).
thf(zip_derived_cl15401,plain,
( ( irel @ ( '#sk8' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl15378,zip_derived_cl175]) ).
thf(zip_derived_cl591_026,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl1154_027,plain,
~ ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1133,zip_derived_cl591,zip_derived_cl595]) ).
thf(zip_derived_cl15426,plain,
irel @ ( '#sk8' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl15401,zip_derived_cl591,zip_derived_cl1154]) ).
thf(zip_derived_cl8_028,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15632,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ X0 @ ( '#sk8' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl15426,zip_derived_cl8]) ).
thf(zip_derived_cl18986,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl15431,zip_derived_cl15632]) ).
thf(zip_derived_cl52,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl73,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl73]) ).
thf(zip_derived_cl99,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk5' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) ) ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl115,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl21,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl25_029,plain,
( '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( f @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a3 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b2 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b1 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a3 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b0 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b3 @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( f @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl29,plain,
! [X2: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl21,zip_derived_cl25]) ).
thf(zip_derived_cl36,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a3 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a3 @ X4 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl54,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b0 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b3 @ Y1 ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk5' @ X2 ) )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) ) ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl169,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ ( '#sk5' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl115,zip_derived_cl75]) ).
thf(zip_derived_cl19012,plain,
( ( irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk5' @ ( '#sk6' @ '#sk1' ) ) )
| ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl18986,zip_derived_cl169]) ).
thf(zip_derived_cl15378_030,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1150,zip_derived_cl1272]) ).
thf(zip_derived_cl148,plain,
! [X2: $i,X4: $i] :
( ~ ( a3 @ ( '#sk12' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl129,plain,
! [X2: $i,X4: $i] :
( ~ ( a3 @ ( '#sk12' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl162,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( a3 @ ( '#sk12' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl148,zip_derived_cl129]) ).
thf(zip_derived_cl15410,plain,
( ~ ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl15378,zip_derived_cl162]) ).
thf(zip_derived_cl591_031,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl1154_032,plain,
~ ( a2 @ ( '#sk11' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1133,zip_derived_cl591,zip_derived_cl595]) ).
thf(zip_derived_cl15435,plain,
~ ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl15410,zip_derived_cl591,zip_derived_cl1154]) ).
thf(zip_derived_cl591_033,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl19037,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk5' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl19012,zip_derived_cl15435,zip_derived_cl591]) ).
thf(zip_derived_cl18986_034,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl15431,zip_derived_cl15632]) ).
thf(zip_derived_cl116,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl99]) ).
thf(zip_derived_cl137,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl145,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk5' @ X2 ) @ ( '#sk9' @ X2 ) )
=> ( b0 @ ( '#sk9' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl137]) ).
thf(zip_derived_cl156,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ ( '#sk9' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i] :
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b3 @ Y0 ) ) ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl88,plain,
! [X2: $i,X4: $i] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl101,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ ( '#sk5' @ X2 ) @ ( '#sk9' @ X2 ) )
=> ( b0 @ ( '#sk9' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl119,plain,
! [X2: $i,X4: $i] :
( ( irel @ ( '#sk5' @ X2 ) @ ( '#sk9' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl178,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ( irel @ ( '#sk5' @ X2 ) @ ( '#sk9' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl156,zip_derived_cl119]) ).
thf(zip_derived_cl19007,plain,
( ( irel @ ( '#sk5' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl18986,zip_derived_cl178]) ).
thf(zip_derived_cl591_035,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl15435_036,plain,
~ ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl15410,zip_derived_cl591,zip_derived_cl1154]) ).
thf(zip_derived_cl19032,plain,
irel @ ( '#sk5' @ ( '#sk6' @ '#sk1' ) ) @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl19007,zip_derived_cl591,zip_derived_cl15435]) ).
thf(zip_derived_cl8_037,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl19266,plain,
! [X0: $i] :
( ( irel @ X0 @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ X0 @ ( '#sk5' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl19032,zip_derived_cl8]) ).
thf(zip_derived_cl23660,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl19037,zip_derived_cl19266]) ).
thf(zip_derived_cl136,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl144,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ ( '#sk6' @ X2 ) @ X6 )
=> ( b0 @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl155,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ ( '#sk6' @ X2 ) @ X6 )
| ( b0 @ X6 )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl144]) ).
thf(zip_derived_cl91,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ ( '#sk6' @ X2 ) @ Y0 )
=> ( b0 @ Y0 ) ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl104,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ ( '#sk6' @ X2 ) @ X6 )
=> ( b0 @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl91]) ).
thf(zip_derived_cl124,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ ( '#sk6' @ X2 ) @ X6 )
| ( b0 @ X6 )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a0 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl173,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a0 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ( b0 @ X6 )
| ~ ( irel @ ( '#sk6' @ X2 ) @ X6 ) ),
inference(clc,[status(thm)],[zip_derived_cl155,zip_derived_cl124]) ).
thf(zip_derived_cl23679,plain,
! [X0: $i] :
( ( b0 @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ '#sk1' )
| ( a0 @ X0 )
| ~ ( irel @ '#sk1' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl23660,zip_derived_cl173]) ).
thf(zip_derived_cl3_038,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl23704,plain,
! [X0: $i] :
( ( b0 @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) )
| ( a0 @ X0 )
| ~ ( irel @ '#sk1' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl23679,zip_derived_cl3]) ).
thf(zip_derived_cl18986_039,plain,
irel @ ( '#sk6' @ '#sk1' ) @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl15431,zip_derived_cl15632]) ).
thf(zip_derived_cl157,plain,
! [X2: $i,X4: $i] :
( ~ ( b0 @ ( '#sk9' @ X2 ) )
| '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl145]) ).
thf(zip_derived_cl120,plain,
! [X2: $i,X4: $i] :
( ~ ( b0 @ ( '#sk9' @ X2 ) )
| ~ '#form3'
| ~ ( irel @ '#sk1' @ X2 )
| ( a3 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl165,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a3 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( b0 @ ( '#sk9' @ X2 ) ) ),
inference(clc,[status(thm)],[zip_derived_cl157,zip_derived_cl120]) ).
thf(zip_derived_cl19016,plain,
( ~ ( b0 @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) )
| ~ ( irel @ '#sk1' @ ( '#sk6' @ '#sk1' ) )
| ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl18986,zip_derived_cl165]) ).
thf(zip_derived_cl591_040,plain,
irel @ '#sk1' @ ( '#sk6' @ '#sk1' ),
inference(demod,[status(thm)],[zip_derived_cl560,zip_derived_cl215,zip_derived_cl3]) ).
thf(zip_derived_cl15435_041,plain,
~ ( a3 @ ( '#sk12' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl15410,zip_derived_cl591,zip_derived_cl1154]) ).
thf(zip_derived_cl19041,plain,
~ ( b0 @ ( '#sk9' @ ( '#sk6' @ '#sk1' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19016,zip_derived_cl591,zip_derived_cl15435]) ).
thf(zip_derived_cl23724,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ( a0 @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl23704,zip_derived_cl19041]) ).
thf(zip_derived_cl23808,plain,
( ~ ( irel @ '#sk1' @ '#sk1' )
| ( a0 @ ( '#sk4' @ '#sk1' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl567,zip_derived_cl23724]) ).
thf(zip_derived_cl3_042,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl215_043,plain,
~ ( a0 @ ( '#sk4' @ '#sk1' ) ),
inference(demod,[status(thm)],[zip_derived_cl209,zip_derived_cl18]) ).
thf(zip_derived_cl23930,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl23808,zip_derived_cl3,zip_derived_cl215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO069^4.003 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.PCqlrOOSHP true
% 0.13/0.35 % Computer : n009.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 08:04:05 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in HO mode
% 0.58/0.67 % Total configuration time : 828
% 0.58/0.67 % Estimated wc time : 1656
% 0.58/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.58/0.72 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.58/0.73 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.59/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.59/0.81 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.60/0.96 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 25.94/3.90 % Solved by lams/30_sp5.sh.
% 25.94/3.90 % done 3512 iterations in 3.040s
% 25.94/3.90 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 25.94/3.90 % SZS output start Refutation
% See solution above
% 25.94/3.91
% 25.94/3.91
% 25.94/3.91 % Terminating...
% 26.75/4.00 % Runner terminated.
% 26.75/4.01 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------