TSTP Solution File: SYN044^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN044^4 : 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.ys4jnYUGzt true
% Computer : n017.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 04:01:17 EDT 2023
% Result : Theorem 7.70s 1.65s
% Output : Refutation 7.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 52
% Syntax : Number of formulae : 248 ( 65 unt; 20 typ; 0 def)
% Number of atoms : 872 ( 33 equ; 17 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2107 ( 271 ~; 314 |; 19 &;1298 @)
% ( 0 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 20 usr; 6 con; 0-3 aty)
% ( 89 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 357 ( 155 ^; 202 !; 0 ?; 357 :)
% Comments :
%------------------------------------------------------------------------------
thf(iatom_type,type,
iatom: ( $i > $o ) > $i > $o ).
thf(r_type,type,
r: $i > $o ).
thf(ivalid_type,type,
ivalid: ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': $i > $i ).
thf(q_type,type,
q: $i > $o ).
thf('#sk4_type',type,
'#sk4': $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(ior_type,type,
ior: ( $i > $o ) > ( $i > $o ) > $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(p_type,type,
p: $i > $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i > $i ).
thf(iequiv_type,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i > $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(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(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('12',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('13',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(pel10_1,axiom,
ivalid @ ( iimplies @ ( iatom @ q ) @ ( iatom @ r ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( r @ X8 ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( q @ X6 ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl12,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( r @ X4 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( r @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk1' @ X2 ) )
=> ( q @ ( '#sk1' @ X2 ) ) )
| ( r @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl18,plain,
! [X2: $i,X4: $i] :
( ~ ( q @ ( '#sk1' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(iequiv,axiom,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ) ).
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('14',plain,
( mand
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
& ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('15',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('16',plain,
( iand
= ( ^ [P: $i > $o,Q: $i > $o] : ( mand @ P @ Q ) ) ),
inference(simplify_rw_rule,[status(thm)],[iand,'15']) ).
thf('17',plain,
( iand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('18',plain,
( iequiv
= ( ^ [P: $i > $o,Q: $i > $o] : ( iand @ ( iimplies @ P @ Q ) @ ( iimplies @ Q @ P ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[iequiv,'11','17','3','9','15','5','7']) ).
thf('19',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(pel10,conjecture,
ivalid @ ( iequiv @ ( iatom @ p ) @ ( iatom @ q ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i] :
( ( ! [X12: $i] :
( ( irel @ X4 @ X12 )
=> ( p @ X12 ) )
| ~ ! [X10: $i] :
( ( irel @ X4 @ X10 )
=> ( q @ X10 ) ) )
& ( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( q @ X8 ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( p @ X6 ) ) ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i] :
( ( ! [X12: $i] :
( ( irel @ X4 @ X12 )
=> ( p @ X12 ) )
| ~ ! [X10: $i] :
( ( irel @ X4 @ X10 )
=> ( q @ X10 ) ) )
& ( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( q @ X8 ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( p @ X6 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl31,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl32,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl33,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl35,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl37,plain,
( ~ ( ( irel @ '#sk3' @ '#sk4' )
=> ( p @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl42,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
=> ( q @ ( '#sk1' @ '#sk3' ) ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl49,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(pel10_2,axiom,
ivalid @ ( iimplies @ ( iatom @ r ) @ ( iand @ ( iatom @ p ) @ ( iatom @ q ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ( q @ X8 )
& ( p @ X8 ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( r @ X6 ) ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( q @ Y1 )
& ( p @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( q @ Y0 )
& ( p @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( q @ X4 )
& ( p @ X4 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( ( q @ X4 )
& ( p @ X4 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i] :
( ( p @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl26,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk2' @ X2 ) )
=> ( r @ ( '#sk2' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( p @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk2' @ X2 ) )
| ( p @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl198,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ( p @ '#sk4' )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl49,zip_derived_cl29]) ).
thf(zip_derived_cl43,plain,
( ~ ( p @ '#sk4' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl46,plain,
( ~ ( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
=> ( q @ ( '#sk1' @ '#sk3' ) ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl51,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl1619,plain,
( ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) )
| ~ ( q @ ( '#sk1' @ '#sk3' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl198,zip_derived_cl51]) ).
thf(zip_derived_cl1642,plain,
( ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( q @ ( '#sk1' @ '#sk3' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl18,zip_derived_cl1619]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( r @ ( '#sk2' @ X2 ) )
| ( p @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl48,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i] :
( ( q @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl25,plain,
! [X2: $i,X4: $i] :
( ~ ( ( irel @ X2 @ ( '#sk2' @ X2 ) )
=> ( r @ ( '#sk2' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( q @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
! [X2: $i,X4: $i] :
( ~ ( r @ ( '#sk2' @ X2 ) )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl103,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( r @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl28]) ).
thf(zip_derived_cl30_001,plain,
! [X2: $i,X4: $i] :
( ~ ( r @ ( '#sk2' @ X2 ) )
| ( p @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl49_002,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl89,plain,
( ( p @ '#sk4' )
| ~ ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( q @ ( '#sk1' @ '#sk3' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl49]) ).
thf(zip_derived_cl51_003,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl157,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( r @ ( '#sk2' @ '#sk3' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl89,zip_derived_cl51]) ).
thf(zip_derived_cl639,plain,
( ~ ( r @ ( '#sk2' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl103,zip_derived_cl157]) ).
thf(zip_derived_cl654,plain,
( ( p @ '#sk4' )
| ~ ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( r @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl30,zip_derived_cl639]) ).
thf(zip_derived_cl673,plain,
( ~ ( r @ ( '#sk2' @ '#sk3' ) )
| ( p @ '#sk4' ) ),
inference(simplify,[status(thm)],[zip_derived_cl654]) ).
thf(zip_derived_cl50,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl28_004,plain,
! [X2: $i,X4: $i] :
( ~ ( r @ ( '#sk2' @ X2 ) )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl84,plain,
( ~ ( p @ '#sk4' )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( r @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl28]) ).
thf(zip_derived_cl51_005,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl189,plain,
( ~ ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl84,zip_derived_cl51]) ).
thf(zip_derived_cl681,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl1669,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( q @ ( '#sk1' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1642,zip_derived_cl681]) ).
thf(zip_derived_cl1670,plain,
~ ( q @ ( '#sk1' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl48_006,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl48_007,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk2' @ X2 ) )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl160,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl27]) ).
thf(zip_derived_cl49_008,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl1197,plain,
( ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl160,zip_derived_cl49]) ).
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_cl6,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl6_009,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl17,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk1' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl114,plain,
! [X0: $i] :
( ( r @ X0 )
| ( irel @ X0 @ ( '#sk1' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl17]) ).
thf(ior,axiom,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf('20',plain,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[ior,'3','5']) ).
thf('21',plain,
( ior
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(pel10_3,axiom,
ivalid @ ( iimplies @ ( iatom @ p ) @ ( ior @ ( iatom @ q ) @ ( iatom @ r ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
( ! [X8: $i] :
( ( irel @ X4 @ X8 )
=> ( ! [X12: $i] :
( ( irel @ X8 @ X12 )
=> ( r @ X12 ) )
| ! [X10: $i] :
( ( irel @ X8 @ X10 )
=> ( q @ X10 ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( p @ X6 ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl55,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( q @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
=> ( r @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( q @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl59,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X4 @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl60,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( ( irel @ X4 @ X8 )
=> ( q @ X8 ) )
| ~ ( irel @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( r @ X6 )
| ~ ( irel @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( irel @ X4 @ X8 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl62,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( ( irel @ X2 @ ( '#sk5' @ X2 ) )
=> ( p @ ( '#sk5' @ X2 ) ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X6 )
| ~ ( irel @ X4 @ X6 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl63,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( irel @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X4 @ X8 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl297,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( r @ X0 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X2 )
| ~ ( irel @ X0 @ X2 )
| ( q @ ( '#sk1' @ X0 ) )
| ( irel @ X1 @ ( '#sk5' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl114,zip_derived_cl63]) ).
thf(zip_derived_cl18_010,plain,
! [X2: $i,X4: $i] :
( ~ ( q @ ( '#sk1' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl6_011,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl137,plain,
! [X0: $i] :
( ( r @ X0 )
| ~ ( q @ ( '#sk1' @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl18,zip_derived_cl6]) ).
thf(zip_derived_cl2676,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( irel @ X1 @ ( '#sk5' @ X1 ) )
| ~ ( irel @ X0 @ X2 )
| ( r @ X2 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl297,zip_derived_cl137]) ).
thf(zip_derived_cl2697,plain,
! [X0: $i,X1: $i] :
( ( r @ X0 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 )
| ( irel @ X1 @ ( '#sk5' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl2676]) ).
thf(zip_derived_cl2726,plain,
! [X0: $i,X1: $i] :
( ( irel @ X1 @ ( '#sk5' @ X1 ) )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl2697]) ).
thf(zip_derived_cl4397,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( r @ ( '#sk2' @ '#sk3' ) )
| ( irel @ '#sk3' @ ( '#sk5' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1197,zip_derived_cl2726]) ).
thf(zip_derived_cl681_012,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl4430,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( irel @ '#sk3' @ ( '#sk5' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4397,zip_derived_cl681]) ).
thf(zip_derived_cl34,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl38,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl39,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl40,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: $i] :
( ( ( irel @ '#sk3' @ X2 )
=> ( q @ X2 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ~ ( irel @ '#sk3' @ X2 )
| ( q @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk3' @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ '#sk3' @ X4 )
=> ( p @ X4 ) )
| ( q @ X2 )
| ~ ( irel @ '#sk3' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk3' @ X4 )
| ( p @ X4 )
| ~ ( irel @ '#sk3' @ X2 )
| ( q @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl4751,plain,
! [X0: $i] :
( ( irel @ '#sk3' @ '#sk4' )
| ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 )
| ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl4430,zip_derived_cl52]) ).
thf(zip_derived_cl6_013,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl114_014,plain,
! [X0: $i] :
( ( r @ X0 )
| ( irel @ X0 @ ( '#sk1' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl17]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( p @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X4 @ X8 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl349,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( r @ X0 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X2 )
| ~ ( irel @ X0 @ X2 )
| ( q @ ( '#sk1' @ X0 ) )
| ~ ( p @ ( '#sk5' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl114,zip_derived_cl64]) ).
thf(zip_derived_cl137_015,plain,
! [X0: $i] :
( ( r @ X0 )
| ~ ( q @ ( '#sk1' @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl18,zip_derived_cl6]) ).
thf(zip_derived_cl3770,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( p @ ( '#sk5' @ X1 ) )
| ~ ( irel @ X0 @ X2 )
| ( r @ X2 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl349,zip_derived_cl137]) ).
thf(zip_derived_cl3787,plain,
! [X0: $i,X1: $i] :
( ( r @ X0 )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 )
| ~ ( p @ ( '#sk5' @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3770]) ).
thf(zip_derived_cl3813,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ ( '#sk5' @ X1 ) )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3787]) ).
thf(zip_derived_cl1197_016,plain,
( ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl160,zip_derived_cl49]) ).
thf(zip_derived_cl3813_017,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ ( '#sk5' @ X1 ) )
| ~ ( irel @ X1 @ X0 )
| ( r @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3787]) ).
thf(zip_derived_cl3839,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1197,zip_derived_cl3813]) ).
thf(zip_derived_cl681_018,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl3886,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ~ ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3839,zip_derived_cl681]) ).
thf(zip_derived_cl29_019,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk2' @ X2 ) )
| ( p @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl3910,plain,
( ~ ( p @ ( '#sk5' @ '#sk3' ) )
| ( p @ '#sk4' )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl3886,zip_derived_cl29]) ).
thf(zip_derived_cl50_020,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl27_021,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk2' @ X2 ) )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl159,plain,
( ~ ( p @ '#sk4' )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl27]) ).
thf(zip_derived_cl51_022,plain,
( ~ ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl1130,plain,
( ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl159,zip_derived_cl51]) ).
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_cl7,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_cl8,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( irel @ X4 @ Y0 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl9,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
=> ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( irel @ X4 @ X6 )
& ( irel @ X2 @ X4 ) )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X4 @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( irel @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl1140,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( irel @ X0 @ ( '#sk2' @ '#sk3' ) )
| ~ ( irel @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1130,zip_derived_cl11]) ).
thf(zip_derived_cl6_023,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl50_024,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl64_025,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ~ ( p @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X4 @ X8 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl345,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ '#sk4' )
| ~ ( irel @ X0 @ '#sk3' )
| ( r @ X1 )
| ~ ( irel @ '#sk3' @ X1 )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ ( '#sk5' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl64]) ).
thf(zip_derived_cl1670_026,plain,
~ ( q @ ( '#sk1' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl3330,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ '#sk4' )
| ~ ( irel @ X0 @ '#sk3' )
| ( r @ X1 )
| ~ ( irel @ '#sk3' @ X1 )
| ~ ( p @ ( '#sk5' @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl345,zip_derived_cl1670]) ).
thf(zip_derived_cl3331,plain,
! [X0: $i] :
( ~ ( p @ ( '#sk5' @ '#sk3' ) )
| ~ ( irel @ '#sk3' @ X0 )
| ( r @ X0 )
| ~ ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl3330]) ).
thf(zip_derived_cl1140_027,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( irel @ X0 @ ( '#sk2' @ '#sk3' ) )
| ~ ( irel @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1130,zip_derived_cl11]) ).
thf(zip_derived_cl17_028,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk1' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl2085,plain,
! [X0: $i] :
( ~ ( irel @ X0 @ '#sk3' )
| ~ ( p @ '#sk4' )
| ( r @ ( '#sk2' @ '#sk3' ) )
| ( irel @ X0 @ ( '#sk1' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1140,zip_derived_cl17]) ).
thf(zip_derived_cl681_029,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl2121,plain,
! [X0: $i] :
( ~ ( irel @ X0 @ '#sk3' )
| ~ ( p @ '#sk4' )
| ( irel @ X0 @ ( '#sk1' @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2085,zip_derived_cl681]) ).
thf(zip_derived_cl1130_030,plain,
( ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(clc,[status(thm)],[zip_derived_cl159,zip_derived_cl51]) ).
thf(zip_derived_cl50_031,plain,
( ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl63_032,plain,
! [X2: $i,X4: $i,X6: $i,X8: $i] :
( ( irel @ X2 @ ( '#sk5' @ X2 ) )
| ~ ( irel @ X4 @ X8 )
| ( q @ X8 )
| ~ ( irel @ X4 @ X6 )
| ( r @ X6 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl293,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ '#sk4' )
| ~ ( irel @ X0 @ '#sk3' )
| ( r @ X1 )
| ~ ( irel @ '#sk3' @ X1 )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ X0 @ ( '#sk5' @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl50,zip_derived_cl63]) ).
thf(zip_derived_cl1670_033,plain,
~ ( q @ ( '#sk1' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl2167,plain,
! [X0: $i,X1: $i] :
( ~ ( p @ '#sk4' )
| ~ ( irel @ X0 @ '#sk3' )
| ( r @ X1 )
| ~ ( irel @ '#sk3' @ X1 )
| ( irel @ X0 @ ( '#sk5' @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl293,zip_derived_cl1670]) ).
thf(zip_derived_cl2171,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( irel @ X0 @ ( '#sk5' @ X0 ) )
| ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( irel @ X0 @ '#sk3' )
| ~ ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1130,zip_derived_cl2167]) ).
thf(zip_derived_cl681_034,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl2209,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( irel @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( irel @ X0 @ '#sk3' )
| ~ ( p @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl2171,zip_derived_cl681]) ).
thf(zip_derived_cl2210,plain,
! [X0: $i] :
( ~ ( irel @ X0 @ '#sk3' )
| ( irel @ X0 @ ( '#sk5' @ X0 ) )
| ~ ( p @ '#sk4' ) ),
inference(simplify,[status(thm)],[zip_derived_cl2209]) ).
thf(zip_derived_cl52_035,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk3' @ X4 )
| ( p @ X4 )
| ~ ( irel @ '#sk3' @ X2 )
| ( q @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl2371,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ~ ( irel @ '#sk3' @ '#sk3' )
| ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 )
| ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl2210,zip_derived_cl52]) ).
thf(zip_derived_cl6_036,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2416,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 )
| ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2371,zip_derived_cl6]) ).
thf(zip_derived_cl2510,plain,
( ~ ( p @ '#sk4' )
| ~ ( irel @ '#sk3' @ '#sk3' )
| ( p @ ( '#sk5' @ '#sk3' ) )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2121,zip_derived_cl2416]) ).
thf(zip_derived_cl6_037,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl1670_038,plain,
~ ( q @ ( '#sk1' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl2567,plain,
( ~ ( p @ '#sk4' )
| ( p @ ( '#sk5' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl2510,zip_derived_cl6,zip_derived_cl1670]) ).
thf(zip_derived_cl2568,plain,
( ( p @ ( '#sk5' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference(simplify,[status(thm)],[zip_derived_cl2567]) ).
thf(zip_derived_cl3339,plain,
! [X0: $i] :
( ~ ( p @ '#sk4' )
| ( r @ X0 )
| ~ ( irel @ '#sk3' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl3331,zip_derived_cl2568]) ).
thf(zip_derived_cl3369,plain,
( ~ ( irel @ '#sk3' @ '#sk3' )
| ~ ( p @ '#sk4' )
| ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1140,zip_derived_cl3339]) ).
thf(zip_derived_cl6_039,plain,
! [X2: $i] : ( irel @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl681_040,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl3433,plain,
( ~ ( p @ '#sk4' )
| ~ ( p @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl3369,zip_derived_cl6,zip_derived_cl681]) ).
thf(zip_derived_cl3434,plain,
~ ( p @ '#sk4' ),
inference(simplify,[status(thm)],[zip_derived_cl3433]) ).
thf(zip_derived_cl3963,plain,
( ~ ( p @ ( '#sk5' @ '#sk3' ) )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3910,zip_derived_cl3434]) ).
thf(zip_derived_cl4015,plain,
( ( r @ ( '#sk2' @ '#sk3' ) )
| ~ ( p @ ( '#sk5' @ '#sk3' ) )
| ~ ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3813,zip_derived_cl3963]) ).
thf(zip_derived_cl681_041,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl4047,plain,
( ~ ( p @ ( '#sk5' @ '#sk3' ) )
| ~ ( p @ ( '#sk5' @ '#sk3' ) ) ),
inference(demod,[status(thm)],[zip_derived_cl4015,zip_derived_cl681]) ).
thf(zip_derived_cl4048,plain,
~ ( p @ ( '#sk5' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl4047]) ).
thf(zip_derived_cl4812,plain,
! [X0: $i] :
( ( irel @ '#sk3' @ '#sk4' )
| ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl4751,zip_derived_cl4048]) ).
thf(zip_derived_cl5095,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( q @ ( '#sk1' @ '#sk3' ) )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl4812]) ).
thf(zip_derived_cl1670_042,plain,
~ ( q @ ( '#sk1' @ '#sk3' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1669]) ).
thf(zip_derived_cl5137,plain,
( ( irel @ '#sk3' @ '#sk4' )
| ( irel @ '#sk3' @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl5095,zip_derived_cl1670]) ).
thf(zip_derived_cl5138,plain,
irel @ '#sk3' @ '#sk4',
inference(simplify,[status(thm)],[zip_derived_cl5137]) ).
thf(zip_derived_cl29_043,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk2' @ X2 ) )
| ( p @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl5184,plain,
( ( p @ '#sk4' )
| ( irel @ '#sk3' @ ( '#sk2' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5138,zip_derived_cl29]) ).
thf(zip_derived_cl3434_044,plain,
~ ( p @ '#sk4' ),
inference(simplify,[status(thm)],[zip_derived_cl3433]) ).
thf(zip_derived_cl5234,plain,
irel @ '#sk3' @ ( '#sk2' @ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl5184,zip_derived_cl3434]) ).
thf(zip_derived_cl17_045,plain,
! [X2: $i,X4: $i] :
( ( irel @ X2 @ ( '#sk1' @ X2 ) )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl5282,plain,
( ( r @ ( '#sk2' @ '#sk3' ) )
| ( irel @ '#sk3' @ ( '#sk1' @ '#sk3' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl5234,zip_derived_cl17]) ).
thf(zip_derived_cl681_046,plain,
~ ( r @ ( '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl673,zip_derived_cl189]) ).
thf(zip_derived_cl5331,plain,
irel @ '#sk3' @ ( '#sk1' @ '#sk3' ),
inference(demod,[status(thm)],[zip_derived_cl5282,zip_derived_cl681]) ).
thf(zip_derived_cl5138_047,plain,
irel @ '#sk3' @ '#sk4',
inference(simplify,[status(thm)],[zip_derived_cl5137]) ).
thf(zip_derived_cl52_048,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ '#sk3' @ X4 )
| ( p @ X4 )
| ~ ( irel @ '#sk3' @ X2 )
| ( q @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl5169,plain,
! [X0: $i] :
( ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 )
| ( p @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl5138,zip_derived_cl52]) ).
thf(zip_derived_cl3434_049,plain,
~ ( p @ '#sk4' ),
inference(simplify,[status(thm)],[zip_derived_cl3433]) ).
thf(zip_derived_cl5227,plain,
! [X0: $i] :
( ( q @ X0 )
| ~ ( irel @ '#sk3' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl5169,zip_derived_cl3434]) ).
thf(zip_derived_cl5541,plain,
q @ ( '#sk1' @ '#sk3' ),
inference('sup-',[status(thm)],[zip_derived_cl5331,zip_derived_cl5227]) ).
thf(zip_derived_cl5626,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl1670,zip_derived_cl5541]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYN044^4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ys4jnYUGzt true
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 18:24:26 EDT 2023
% 0.20/0.33 % CPUTime :
% 0.20/0.33 % Running portfolio for 300 s
% 0.20/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.34 % Number of cores: 8
% 0.20/0.34 % Python version: Python 3.6.8
% 0.20/0.34 % Running in HO mode
% 0.20/0.65 % Total configuration time : 828
% 0.20/0.65 % Estimated wc time : 1656
% 0.20/0.65 % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.33/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.33/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.40/0.75 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.40/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.40/0.77 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.40/0.77 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.40/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.47/0.83 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 7.70/1.65 % Solved by lams/30_sp5.sh.
% 7.70/1.65 % done 1192 iterations in 0.855s
% 7.70/1.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 7.70/1.65 % SZS output start Refutation
% See solution above
% 7.70/1.65
% 7.70/1.65
% 7.70/1.65 % Terminating...
% 8.99/1.78 % Runner terminated.
% 8.99/1.79 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------