TSTP Solution File: SYN393^4.002 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN393^4.002 : 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.qaCfdQ6Svy true
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 04:03:13 EDT 2023
% Result : Theorem 1.22s 0.84s
% Output : Refutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 76
% Syntax : Number of formulae : 261 ( 43 unt; 24 typ; 0 def)
% Number of atoms : 1793 ( 30 equ; 136 cnn)
% Maximal formula atoms : 67 ( 7 avg)
% Number of connectives : 3974 ( 476 ~; 516 |; 67 &;2140 @)
% ( 0 <=>; 418 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 97 ( 97 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 11 con; 0-3 aty)
% ( 357 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 574 ( 417 ^; 157 !; 0 ?; 574 :)
% Comments :
%------------------------------------------------------------------------------
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf('#form3_type',type,
'#form3': $o ).
thf(a2_type,type,
a2: $i > $o ).
thf('#sk6_type',type,
'#sk6': $i ).
thf('#sk1_type',type,
'#sk1': $i ).
thf(irel_type,type,
irel: $i > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form8_type',type,
'#form8': $i > $o ).
thf('#form10_type',type,
'#form10': $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(iimplies_type,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a1_type,type,
a1: $i > $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk9_type',type,
'#sk9': $i > $i ).
thf('#form5_type',type,
'#form5': $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk11_type',type,
'#sk11': $i > $i ).
thf('#sk7_type',type,
'#sk7': $i ).
thf(iequiv_type,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(ivalid,axiom,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( ivalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[ivalid]) ).
thf('1',plain,
( ivalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(iequiv,axiom,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
thf(iimplies,axiom,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ) ).
thf('2',plain,
( mbox_s4
= ( ^ [P: $i > $o,X: $i] :
! [Y: $i] :
( ( irel @ X @ Y )
=> ( P @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('3',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( irel @ V_2 @ X4 )
=> ( V_1 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ) ).
thf('4',plain,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('5',plain,
( mor
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
| ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('7',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('8',plain,
( mimplies
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'5','7']) ).
thf('9',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( iimplies
= ( ^ [P: $i > $o,Q: $i > $o] : ( mimplies @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iimplies,'3','9']) ).
thf('11',plain,
( iimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mimplies @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(iand,axiom,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ) ).
thf(mand,axiom,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ) ).
thf('12',plain,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
& ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
inference(simplify_rw_rule,[status(thm)],[iand,'13']) ).
thf('15',plain,
( iand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('16',plain,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iequiv,'11','15','3','9','13','5','7']) ).
thf('17',plain,
( iequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( iand @ ( iimplies @ V_1 @ V_2 ) @ ( iimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('18',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('19',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(con,conjecture,
ivalid @ ( iequiv @ ( iequiv @ ( iatom @ a1 ) @ ( iatom @ a2 ) ) @ ( iequiv @ ( iatom @ a2 ) @ ( iatom @ a1 ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( ! [X36: $i] :
( ( irel @ X4 @ X36 )
=> ( ( ! [X44: $i] :
( ( irel @ X36 @ X44 )
=> ( a1 @ X44 ) )
| ~ ! [X42: $i] :
( ( irel @ X36 @ X42 )
=> ( a2 @ X42 ) ) )
& ( ! [X40: $i] :
( ( irel @ X36 @ X40 )
=> ( a2 @ X40 ) )
| ~ ! [X38: $i] :
( ( irel @ X36 @ X38 )
=> ( a1 @ X38 ) ) ) ) )
| ~ ! [X26: $i] :
( ( irel @ X4 @ X26 )
=> ( ( ! [X34: $i] :
( ( irel @ X26 @ X34 )
=> ( a2 @ X34 ) )
| ~ ! [X32: $i] :
( ( irel @ X26 @ X32 )
=> ( a1 @ X32 ) ) )
& ( ! [X30: $i] :
( ( irel @ X26 @ X30 )
=> ( a1 @ X30 ) )
| ~ ! [X28: $i] :
( ( irel @ X26 @ X28 )
=> ( a2 @ X28 ) ) ) ) ) )
& ( ! [X16: $i] :
( ( irel @ X4 @ X16 )
=> ( ( ! [X24: $i] :
( ( irel @ X16 @ X24 )
=> ( a2 @ X24 ) )
| ~ ! [X22: $i] :
( ( irel @ X16 @ X22 )
=> ( a1 @ X22 ) ) )
& ( ! [X20: $i] :
( ( irel @ X16 @ X20 )
=> ( a1 @ X20 ) )
| ~ ! [X18: $i] :
( ( irel @ X16 @ X18 )
=> ( a2 @ X18 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X14: $i] :
( ( irel @ X6 @ X14 )
=> ( a1 @ X14 ) )
| ~ ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ( a2 @ X12 ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( a2 @ X10 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( a1 @ X8 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( ! [X36: $i] :
( ( irel @ X4 @ X36 )
=> ( ( ! [X44: $i] :
( ( irel @ X36 @ X44 )
=> ( a1 @ X44 ) )
| ~ ! [X42: $i] :
( ( irel @ X36 @ X42 )
=> ( a2 @ X42 ) ) )
& ( ! [X40: $i] :
( ( irel @ X36 @ X40 )
=> ( a2 @ X40 ) )
| ~ ! [X38: $i] :
( ( irel @ X36 @ X38 )
=> ( a1 @ X38 ) ) ) ) )
| ~ ! [X26: $i] :
( ( irel @ X4 @ X26 )
=> ( ( ! [X34: $i] :
( ( irel @ X26 @ X34 )
=> ( a2 @ X34 ) )
| ~ ! [X32: $i] :
( ( irel @ X26 @ X32 )
=> ( a1 @ X32 ) ) )
& ( ! [X30: $i] :
( ( irel @ X26 @ X30 )
=> ( a1 @ X30 ) )
| ~ ! [X28: $i] :
( ( irel @ X26 @ X28 )
=> ( a2 @ X28 ) ) ) ) ) )
& ( ! [X16: $i] :
( ( irel @ X4 @ X16 )
=> ( ( ! [X24: $i] :
( ( irel @ X16 @ X24 )
=> ( a2 @ X24 ) )
| ~ ! [X22: $i] :
( ( irel @ X16 @ X22 )
=> ( a1 @ X22 ) ) )
& ( ! [X20: $i] :
( ( irel @ X16 @ X20 )
=> ( a1 @ X20 ) )
| ~ ! [X18: $i] :
( ( irel @ X16 @ X18 )
=> ( a2 @ X18 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ( ! [X14: $i] :
( ( irel @ X6 @ X14 )
=> ( a1 @ X14 ) )
| ~ ! [X12: $i] :
( ( irel @ X6 @ X12 )
=> ( a2 @ X12 ) ) )
& ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( a2 @ X10 ) )
| ~ ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( a1 @ X8 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a2 @ Y2 ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl8,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ '#form5' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl3,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl5,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl6,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
( ~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl12,plain,
( ( irel @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl16,plain,
( ~ ( ( irel @ '#sk1' @ '#sk4' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl28,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl50,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl51,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl52,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ( ( irel @ '#sk4' @ X2 )
=> ( a1 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24_001,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl20,zip_derived_cl24]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl60,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl77,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl59,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl58,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl74,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl19_002,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl24_003,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl19,zip_derived_cl24]) ).
thf(zip_derived_cl31,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl71,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl90,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl77,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl21,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl215,plain,
( ( '#form8' @ '#sk4' )
| ~ '#form5'
| ~ ( '#form10' @ '#sk4' )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl90,zip_derived_cl21]) ).
thf(zip_derived_cl58_004,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl74_005,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71_006,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl76,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl58,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl65_007,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_008,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl88,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form10' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl76,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl21_009,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl137,plain,
( ( '#form10' @ '#sk4' )
| ~ '#form5'
| ~ ( '#form8' @ '#sk4' )
| '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl21]) ).
thf(zip_derived_cl34,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl47,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl48,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
( ~ ( ( irel @ '#sk4' @ '#sk7' )
=> ( a2 @ '#sk7' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl63,plain,
( ( irel @ '#sk4' @ '#sk7' )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl74_010,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71_011,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl81,plain,
( ~ ( '#form10' @ '#sk4' )
| '#form3'
| ( irel @ '#sk4' @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl63,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl65_012,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a2 @ X4 ) )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl91,plain,
( '#form3'
| ~ ( '#form10' @ '#sk4' )
| ~ ( '#form8' @ '#sk4' )
| ( a2 @ '#sk7' ) ),
inference('sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl84]) ).
thf(zip_derived_cl64,plain,
( ~ ( a2 @ '#sk7' )
| '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl74_013,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl71_014,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl82,plain,
( ~ ( '#form10' @ '#sk4' )
| '#form3'
| ~ ( a2 @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl64,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl105,plain,
( ~ ( '#form8' @ '#sk4' )
| ~ ( '#form10' @ '#sk4' )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl91,zip_derived_cl82]) ).
thf(zip_derived_cl153,plain,
( '#form3'
| ~ ( '#form8' @ '#sk4' )
| ~ '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl137,zip_derived_cl105]) ).
thf(zip_derived_cl235,plain,
( '#form3'
| ~ ( '#form10' @ '#sk4' )
| ~ '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl215,zip_derived_cl153]) ).
thf(zip_derived_cl81_015,plain,
( ~ ( '#form10' @ '#sk4' )
| '#form3'
| ( irel @ '#sk4' @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl63,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl21_016,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl57_017,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl71_018,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl73,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form10' @ X2 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl57,zip_derived_cl71]) ).
thf(zip_derived_cl107,plain,
! [X0: $i] :
( '#form3'
| ~ ( irel @ '#sk4' @ X0 )
| ( a2 @ X0 )
| '#form5'
| ~ ( '#form10' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl73]) ).
thf(zip_derived_cl125,plain,
( '#form3'
| ~ ( '#form10' @ '#sk4' )
| ~ ( '#form10' @ '#sk4' )
| '#form5'
| ( a2 @ '#sk7' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl107]) ).
thf(zip_derived_cl131,plain,
( ( a2 @ '#sk7' )
| '#form5'
| ~ ( '#form10' @ '#sk4' )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl125]) ).
thf(zip_derived_cl82_019,plain,
( ~ ( '#form10' @ '#sk4' )
| '#form3'
| ~ ( a2 @ '#sk7' ) ),
inference(renaming,[status(thm)],[zip_derived_cl64,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl133,plain,
( '#form3'
| ~ ( '#form10' @ '#sk4' )
| '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl131,zip_derived_cl82]) ).
thf(zip_derived_cl236,plain,
( ~ ( '#form10' @ '#sk4' )
| '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl235,zip_derived_cl133]) ).
thf(zip_derived_cl60_020,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ~ ( ( irel @ X2 @ ( '#sk9' @ X2 ) )
=> ( a2 @ ( '#sk9' @ X2 ) ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl79,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl12_021,plain,
( ( irel @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15_022,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl17,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl73_023,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form10' @ X2 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( a2 @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(renaming,[status(thm)],[zip_derived_cl57,zip_derived_cl71]) ).
thf(zip_derived_cl108,plain,
! [X0: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk2' @ X0 )
| ( a2 @ X0 )
| '#form5'
| ~ ( '#form10' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl73]) ).
thf(zip_derived_cl90_024,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form8' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl77,zip_derived_cl74,zip_derived_cl71]) ).
thf(zip_derived_cl17_025,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl216,plain,
( ( '#form8' @ '#sk2' )
| ~ '#form5'
| ~ ( '#form10' @ '#sk2' )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl90,zip_derived_cl17]) ).
thf(zip_derived_cl88_026,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( '#form10' @ X2 ) ),
inference(renaming,[status(thm)],[zip_derived_cl76,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl17_027,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl138,plain,
( ( '#form10' @ '#sk2' )
| ~ '#form5'
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference('sup+',[status(thm)],[zip_derived_cl88,zip_derived_cl17]) ).
thf(zip_derived_cl13,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15_028,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a1 @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a2 @ Y1 ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl18,plain,
( ~ '#form3'
| ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl13,zip_derived_cl15]) ).
thf(zip_derived_cl23,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl29,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl37,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( irel @ '#sk2' @ '#sk6' )
=> ( a1 @ '#sk6' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl54,plain,
( ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl65_029,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_030,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl68,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( irel @ '#sk2' @ '#sk6' ) ),
inference(renaming,[status(thm)],[zip_derived_cl54,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl74_031,plain,
! [X2: $i] :
( ~ ( '#form10' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) )
| ~ ( '#form10' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl178,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form10' @ '#sk2' )
| ( a1 @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl89]) ).
thf(zip_derived_cl55,plain,
( ~ ( a1 @ '#sk6' )
| ~ '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl65_032,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_033,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl69,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( a1 @ '#sk6' ) ),
inference(renaming,[status(thm)],[zip_derived_cl55,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl199,plain,
( ~ ( '#form10' @ '#sk2' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl178,zip_derived_cl69]) ).
thf(zip_derived_cl201,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ '#form5'
| ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl138,zip_derived_cl199]) ).
thf(zip_derived_cl204,plain,
( ~ '#form5'
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl201]) ).
thf(zip_derived_cl68_034,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( irel @ '#sk2' @ '#sk6' ) ),
inference(renaming,[status(thm)],[zip_derived_cl54,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl46_035,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl60_036,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i] :
( ~ ( '#form8' @ X2 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5'
| ( ( irel @ X2 @ X4 )
=> ( a1 @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl46,zip_derived_cl60]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl158,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( '#form8' @ '#sk2' )
| ~ ( irel @ '#sk1' @ '#sk2' )
| '#form5'
| ( a1 @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl78]) ).
thf(zip_derived_cl169,plain,
( ( a1 @ '#sk6' )
| '#form5'
| ~ ( irel @ '#sk1' @ '#sk2' )
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl69_037,plain,
( ~ ( '#form8' @ '#sk2' )
| ~ '#form3'
| ~ ( a1 @ '#sk6' ) ),
inference(renaming,[status(thm)],[zip_derived_cl55,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl171,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' )
| ~ ( irel @ '#sk1' @ '#sk2' )
| '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl169,zip_derived_cl69]) ).
thf(zip_derived_cl17_038,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl172,plain,
( '#form5'
| ~ ( '#form8' @ '#sk2' )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl171,zip_derived_cl17]) ).
thf(zip_derived_cl208,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl204,zip_derived_cl172]) ).
thf(zip_derived_cl231,plain,
( ~ '#form3'
| ~ ( '#form10' @ '#sk2' )
| ~ '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl216,zip_derived_cl208]) ).
thf(zip_derived_cl237,plain,
! [X0: $i] :
( ~ ( '#form10' @ '#sk2' )
| ( a2 @ X0 )
| ~ ( irel @ '#sk2' @ X0 )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl231]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ~ ( a2 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl238,plain,
! [X0: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk2' @ ( '#sk9' @ X0 ) )
| ~ ( '#form10' @ '#sk2' )
| ( '#form8' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl237,zip_derived_cl80]) ).
thf(zip_derived_cl79_039,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl71_040,plain,
! [X2: $i] :
( ( '#form10' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl72,plain,
! [X2: $i] :
( ~ ( ( irel @ X2 @ ( '#sk11' @ X2 ) )
=> ( a1 @ ( '#sk11' @ X2 ) ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl86,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl30,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl39,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl40,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a2 @ Y0 ) ) )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( ( irel @ '#sk2' @ X2 )
=> ( a2 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X2: $i] :
( ~ ( irel @ '#sk2' @ X2 )
| ( a2 @ X2 )
| ~ '#form3'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( a1 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ '#sk2' @ X4 )
=> ( a1 @ X4 ) )
| ~ '#form3'
| ( a2 @ X2 )
| ~ ( irel @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk2' @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk2' @ X2 )
| ( a2 @ X2 )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl192,plain,
! [X0: $i] :
( ( '#form10' @ '#sk2' )
| ~ '#form3'
| ( a2 @ X0 )
| ~ ( irel @ '#sk2' @ X0 )
| ( a1 @ ( '#sk11' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl85]) ).
thf(zip_derived_cl237_041,plain,
! [X0: $i] :
( ~ ( '#form10' @ '#sk2' )
| ( a2 @ X0 )
| ~ ( irel @ '#sk2' @ X0 )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl108,zip_derived_cl231]) ).
thf(zip_derived_cl242,plain,
! [X0: $i] :
( ( a1 @ ( '#sk11' @ '#sk2' ) )
| ~ ( irel @ '#sk2' @ X0 )
| ( a2 @ X0 )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl192,zip_derived_cl237]) ).
thf(zip_derived_cl244,plain,
( ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( a2 @ ( '#sk9' @ '#sk2' ) )
| ( a1 @ ( '#sk11' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl242]) ).
thf(zip_derived_cl208_042,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl204,zip_derived_cl172]) ).
thf(zip_derived_cl248,plain,
( ( a1 @ ( '#sk11' @ '#sk2' ) )
| ( a2 @ ( '#sk9' @ '#sk2' ) )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl244,zip_derived_cl208]) ).
thf(zip_derived_cl80_043,plain,
! [X2: $i] :
( ~ ( a2 @ ( '#sk9' @ X2 ) )
| ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl249,plain,
( ~ '#form3'
| ( a1 @ ( '#sk11' @ '#sk2' ) )
| ( '#form8' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl248,zip_derived_cl80]) ).
thf(zip_derived_cl208_044,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl204,zip_derived_cl172]) ).
thf(zip_derived_cl253,plain,
( ( a1 @ ( '#sk11' @ '#sk2' ) )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl249,zip_derived_cl208]) ).
thf(zip_derived_cl87,plain,
! [X2: $i] :
( ~ ( a1 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl254,plain,
( ~ '#form3'
| ( '#form10' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl253,zip_derived_cl87]) ).
thf(zip_derived_cl344,plain,
! [X0: $i] :
( ( '#form8' @ X0 )
| ~ ( irel @ '#sk2' @ ( '#sk9' @ X0 ) )
| ~ '#form3' ),
inference(clc,[status(thm)],[zip_derived_cl238,zip_derived_cl254]) ).
thf(zip_derived_cl346,plain,
( ( '#form8' @ '#sk2' )
| ~ '#form3'
| ( '#form8' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl344]) ).
thf(zip_derived_cl349,plain,
( ~ '#form3'
| ( '#form8' @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl346]) ).
thf(zip_derived_cl208_045,plain,
( ~ '#form3'
| ~ ( '#form8' @ '#sk2' ) ),
inference(clc,[status(thm)],[zip_derived_cl204,zip_derived_cl172]) ).
thf(zip_derived_cl353,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl349,zip_derived_cl208]) ).
thf(zip_derived_cl361,plain,
~ ( '#form10' @ '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl236,zip_derived_cl353]) ).
thf(zip_derived_cl21_046,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl353_047,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl349,zip_derived_cl208]) ).
thf(zip_derived_cl354,plain,
irel @ '#sk1' @ '#sk4',
inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl353]) ).
thf(zip_derived_cl86_048,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl78_049,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl153_050,plain,
( '#form3'
| ~ ( '#form8' @ '#sk4' )
| ~ '#form5' ),
inference(clc,[status(thm)],[zip_derived_cl137,zip_derived_cl105]) ).
thf(zip_derived_cl353_051,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl349,zip_derived_cl208]) ).
thf(zip_derived_cl358,plain,
( ~ ( '#form8' @ '#sk4' )
| ~ '#form5' ),
inference(demod,[status(thm)],[zip_derived_cl153,zip_derived_cl353]) ).
thf(zip_derived_cl86_052,plain,
! [X2: $i] :
( ( irel @ X2 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl53_053,plain,
! [X2: $i] :
( ( ( irel @ '#sk4' @ X2 )
=> ( a1 @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( a2 @ Y0 ) ) )
| '#form3' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl65_054,plain,
! [X2: $i] :
( ~ ( '#form8' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60_055,plain,
! [X2: $i] :
( ( '#form8' @ X2 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl67,plain,
! [X2: $i] :
( ( '#form8' @ '#sk4' )
| '#form3'
| ( ( irel @ '#sk4' @ X2 )
=> ( a1 @ X2 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl53,zip_derived_cl65,zip_derived_cl60]) ).
thf(zip_derived_cl83,plain,
! [X2: $i] :
( ~ ( irel @ '#sk4' @ X2 )
| ( a1 @ X2 )
| '#form3'
| ( '#form8' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl353_056,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl349,zip_derived_cl208]) ).
thf(zip_derived_cl355,plain,
! [X2: $i] :
( ~ ( irel @ '#sk4' @ X2 )
| ( a1 @ X2 )
| ( '#form8' @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl83,zip_derived_cl353]) ).
thf(zip_derived_cl387,plain,
( ( '#form10' @ '#sk4' )
| ( '#form8' @ '#sk4' )
| ( a1 @ ( '#sk11' @ '#sk4' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl355]) ).
thf(zip_derived_cl361_057,plain,
~ ( '#form10' @ '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl236,zip_derived_cl353]) ).
thf(zip_derived_cl391,plain,
( ( '#form8' @ '#sk4' )
| ( a1 @ ( '#sk11' @ '#sk4' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl387,zip_derived_cl361]) ).
thf(zip_derived_cl87_058,plain,
! [X2: $i] :
( ~ ( a1 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl398,plain,
( ( '#form8' @ '#sk4' )
| ( '#form10' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl391,zip_derived_cl87]) ).
thf(zip_derived_cl361_059,plain,
~ ( '#form10' @ '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl236,zip_derived_cl353]) ).
thf(zip_derived_cl402,plain,
'#form8' @ '#sk4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl361]) ).
thf(zip_derived_cl403,plain,
~ '#form5',
inference(demod,[status(thm)],[zip_derived_cl358,zip_derived_cl402]) ).
thf(zip_derived_cl405,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( a1 @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ ( '#form8' @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl78,zip_derived_cl403]) ).
thf(zip_derived_cl428,plain,
! [X0: $i] :
( ( '#form10' @ X0 )
| ~ ( '#form8' @ X0 )
| ~ ( irel @ '#sk1' @ X0 )
| ( a1 @ ( '#sk11' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl405]) ).
thf(zip_derived_cl87_060,plain,
! [X2: $i] :
( ~ ( a1 @ ( '#sk11' @ X2 ) )
| ( '#form10' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl433,plain,
! [X0: $i] :
( ~ ( irel @ '#sk1' @ X0 )
| ~ ( '#form8' @ X0 )
| ( '#form10' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl428,zip_derived_cl87]) ).
thf(zip_derived_cl437,plain,
( ( '#form10' @ '#sk4' )
| ~ ( '#form8' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl354,zip_derived_cl433]) ).
thf(zip_derived_cl402_061,plain,
'#form8' @ '#sk4',
inference(clc,[status(thm)],[zip_derived_cl398,zip_derived_cl361]) ).
thf(zip_derived_cl446,plain,
'#form10' @ '#sk4',
inference(demod,[status(thm)],[zip_derived_cl437,zip_derived_cl402]) ).
thf(zip_derived_cl450,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl361,zip_derived_cl446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.10 % Problem : SYN393^4.002 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.qaCfdQ6Svy true
% 0.11/0.32 % Computer : n023.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Aug 26 19:27:56 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.33 % Python version: Python 3.6.8
% 0.11/0.33 % Running in HO mode
% 0.18/0.59 % Total configuration time : 828
% 0.18/0.59 % Estimated wc time : 1656
% 0.18/0.59 % Estimated cpu time (8 cpus) : 207.0
% 0.96/0.62 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.00/0.65 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.00/0.65 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.00/0.65 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.00/0.65 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.00/0.66 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.00/0.66 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.00/0.68 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.22/0.84 % Solved by lams/20_acsne_simpl.sh.
% 1.22/0.84 % done 145 iterations in 0.128s
% 1.22/0.84 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.22/0.84 % SZS output start Refutation
% See solution above
% 1.22/0.85
% 1.22/0.85
% 1.22/0.85 % Terminating...
% 1.48/0.89 % Runner terminated.
% 1.48/0.90 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------