TSTP Solution File: SYN045^4 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYN045^4 : 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.aeFVvPX4zf true
% Computer : n012.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 1.43s 0.87s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 59
% Syntax : Number of formulae : 192 ( 46 unt; 26 typ; 0 def)
% Number of atoms : 1247 ( 33 equ; 11 cnn)
% Maximal formula atoms : 49 ( 7 avg)
% Number of connectives : 2716 ( 219 ~; 360 |; 73 &;1510 @)
% ( 0 <=>; 302 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 105 ( 105 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 15 con; 0-3 aty)
% ( 252 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 441 ( 318 ^; 123 !; 0 ?; 441 :)
% 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('#sk6_type',type,
'#sk6': $i ).
thf(q_type,type,
q: $i > $o ).
thf('#sk9_type',type,
'#sk9': $i ).
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('#sk11_type',type,
'#sk11': $i ).
thf(ior_type,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
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('#form3_type',type,
'#form3': $o ).
thf(iand_type,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#form10_type',type,
'#form10': $o ).
thf(iequiv_type,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form5_type',type,
'#form5': $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk7_type',type,
'#sk7': $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(ior,axiom,
( ior
= ( ^ [P: $i > $o,Q: $i > $o] : ( mor @ ( mbox_s4 @ P ) @ ( mbox_s4 @ Q ) ) ) ) ).
thf('18',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('19',plain,
( ior
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mbox_s4 @ V_1 ) @ ( mbox_s4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(iatom,axiom,
( iatom
= ( ^ [P: $i > $o] : P ) ) ).
thf('20',plain,
( iatom
= ( ^ [P: $i > $o] : P ) ),
inference(simplify_rw_rule,[status(thm)],[iatom]) ).
thf('21',plain,
( iatom
= ( ^ [V_1: $i > $o] : V_1 ) ),
define([status(thm)]) ).
thf(pel13,conjecture,
ivalid @ ( iequiv @ ( ior @ ( iatom @ p ) @ ( iand @ ( iatom @ q ) @ ( iatom @ r ) ) ) @ ( iand @ ( ior @ ( iatom @ p ) @ ( iatom @ q ) ) @ ( ior @ ( iatom @ p ) @ ( iatom @ r ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i] :
( ( ! [X32: $i] :
( ( irel @ X4 @ X32 )
=> ( ! [X36: $i] :
( ( irel @ X32 @ X36 )
=> ( ( r @ X36 )
& ( q @ X36 ) ) )
| ! [X34: $i] :
( ( irel @ X32 @ X34 )
=> ( p @ X34 ) ) ) )
| ~ ! [X22: $i] :
( ( irel @ X4 @ X22 )
=> ( ( ! [X30: $i] :
( ( irel @ X22 @ X30 )
=> ( r @ X30 ) )
| ! [X28: $i] :
( ( irel @ X22 @ X28 )
=> ( p @ X28 ) ) )
& ( ! [X26: $i] :
( ( irel @ X22 @ X26 )
=> ( q @ X26 ) )
| ! [X24: $i] :
( ( irel @ X22 @ X24 )
=> ( p @ X24 ) ) ) ) ) )
& ( ! [X12: $i] :
( ( irel @ X4 @ X12 )
=> ( ( ! [X20: $i] :
( ( irel @ X12 @ X20 )
=> ( r @ X20 ) )
| ! [X18: $i] :
( ( irel @ X12 @ X18 )
=> ( p @ X18 ) ) )
& ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( q @ X16 ) )
| ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( p @ X14 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( ( r @ X10 )
& ( q @ X10 ) ) )
| ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( p @ X8 ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i] :
( ( ! [X32: $i] :
( ( irel @ X4 @ X32 )
=> ( ! [X36: $i] :
( ( irel @ X32 @ X36 )
=> ( ( r @ X36 )
& ( q @ X36 ) ) )
| ! [X34: $i] :
( ( irel @ X32 @ X34 )
=> ( p @ X34 ) ) ) )
| ~ ! [X22: $i] :
( ( irel @ X4 @ X22 )
=> ( ( ! [X30: $i] :
( ( irel @ X22 @ X30 )
=> ( r @ X30 ) )
| ! [X28: $i] :
( ( irel @ X22 @ X28 )
=> ( p @ X28 ) ) )
& ( ! [X26: $i] :
( ( irel @ X22 @ X26 )
=> ( q @ X26 ) )
| ! [X24: $i] :
( ( irel @ X22 @ X24 )
=> ( p @ X24 ) ) ) ) ) )
& ( ! [X12: $i] :
( ( irel @ X4 @ X12 )
=> ( ( ! [X20: $i] :
( ( irel @ X12 @ X20 )
=> ( r @ X20 ) )
| ! [X18: $i] :
( ( irel @ X12 @ X18 )
=> ( p @ X18 ) ) )
& ( ! [X16: $i] :
( ( irel @ X12 @ X16 )
=> ( q @ X16 ) )
| ! [X14: $i] :
( ( irel @ X12 @ X14 )
=> ( p @ X14 ) ) ) ) )
| ~ ! [X6: $i] :
( ( irel @ X4 @ X6 )
=> ( ! [X10: $i] :
( ( irel @ X6 @ X10 )
=> ( ( r @ X10 )
& ( q @ X10 ) ) )
| ! [X8: $i] :
( ( irel @ X6 @ X8 )
=> ( p @ 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 )
=> ( ( r @ Y2 )
& ( q @ Y2 ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( r @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) )
& ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( q @ Y2 ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( r @ Y2 )
& ( q @ Y2 ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
( ~ ( ( irel @ '#sk1' @ '#sk2' )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl16,plain,
( ~ ( ( irel @ '#sk1' @ '#sk4' )
=> ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl22,plain,
( ~ ( ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl29,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl45,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| $true ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl46,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) )
| '#form3' ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl47,plain,
( ~ ( ( irel @ '#sk4' @ '#sk9' )
=> ( p @ '#sk9' ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl54,plain,
( ( irel @ '#sk4' @ '#sk9' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl13,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( p @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15_001,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl18,plain,
( ~ '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl13,zip_derived_cl15]) ).
thf(zip_derived_cl24,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( p @ Y0 ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl31,plain,
( ~ ( ( irel @ '#sk2' @ '#sk7' )
=> ( p @ '#sk7' ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl39,plain,
( ( irel @ '#sk2' @ '#sk7' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl12_002,plain,
( ( irel @ '#sk1' @ '#sk2' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl15_003,plain,
( '#form3'
| ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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_cl4,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl9,plain,
( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) )
& ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( q @ Y1 ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ 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 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) )
& ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl20,zip_derived_cl25]) ).
thf(zip_derived_cl34,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( q @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( q @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl58,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl67,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( q @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl25_004,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( ( ( irel @ '#sk1' @ X2 )
=> ( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ) )
| ~ '#form5' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( ( r @ X4 )
& ( q @ X4 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl57,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( ( r @ X4 )
& ( q @ X4 ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: $i] :
( ( q @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl71,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( q @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p @ X6 )
| ( q @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl79,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X6 ) ),
inference(clc,[status(thm)],[zip_derived_cl67,zip_derived_cl77]) ).
thf(zip_derived_cl104,plain,
! [X0: $i,X1: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk2' @ X0 )
| ( p @ X0 )
| ~ ( irel @ '#sk2' @ X1 )
| ( q @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl79]) ).
thf(zip_derived_cl139,plain,
! [X0: $i] :
( ~ '#form3'
| ( q @ X0 )
| ~ ( irel @ '#sk2' @ X0 )
| ( p @ '#sk7' )
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl104]) ).
thf(zip_derived_cl143,plain,
! [X0: $i] :
( ( p @ '#sk7' )
| ~ ( irel @ '#sk2' @ X0 )
| ( q @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl139]) ).
thf(zip_derived_cl40,plain,
( ~ ( p @ '#sk7' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl147,plain,
! [X0: $i] :
( ~ '#form3'
| ( q @ X0 )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl143,zip_derived_cl40]) ).
thf(zip_derived_cl39_005,plain,
( ( irel @ '#sk2' @ '#sk7' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl17_006,plain,
( ~ '#form3'
| ( irel @ '#sk1' @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl12,zip_derived_cl15]) ).
thf(zip_derived_cl19_007,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) )
| ~ ( irel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl25_008,plain,
( ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk1' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( r @ Y1 )
& ( q @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p @ Y1 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] :
( '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl19,zip_derived_cl25]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( r @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i] :
( ( ( irel @ X2 @ X4 )
=> ( r @ X4 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: $i] :
( ~ ( irel @ X2 @ X4 )
| ( r @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl56,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) )
| '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( r @ X4 )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl64,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X4 )
| ( r @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| '#form5' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl65,plain,
! [X2: $i,X4: $i] :
( ( r @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ( !!
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( p @ Y0 ) ) )
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl70,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( irel @ X2 @ X6 )
=> ( p @ X6 ) )
| ~ ( irel @ X2 @ X4 )
| ~ '#form5'
| ~ ( irel @ '#sk1' @ X2 )
| ( r @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ X2 @ X6 )
| ( p @ X6 )
| ( r @ X4 )
| ~ ( irel @ '#sk1' @ X2 )
| ~ '#form5'
| ~ ( irel @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( r @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X6 ) ),
inference(clc,[status(thm)],[zip_derived_cl64,zip_derived_cl76]) ).
thf(zip_derived_cl81,plain,
! [X0: $i,X1: $i] :
( ~ '#form3'
| ~ ( irel @ '#sk2' @ X0 )
| ( p @ X0 )
| ~ ( irel @ '#sk2' @ X1 )
| ( r @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl17,zip_derived_cl78]) ).
thf(zip_derived_cl84,plain,
! [X0: $i] :
( ~ '#form3'
| ( r @ X0 )
| ~ ( irel @ '#sk2' @ X0 )
| ( p @ '#sk7' )
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl81]) ).
thf(zip_derived_cl88,plain,
! [X0: $i] :
( ( p @ '#sk7' )
| ~ ( irel @ '#sk2' @ X0 )
| ( r @ X0 )
| ~ '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl40_009,plain,
( ~ ( p @ '#sk7' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl92,plain,
! [X0: $i] :
( ~ '#form3'
| ( r @ X0 )
| ~ ( irel @ '#sk2' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl88,zip_derived_cl40]) ).
thf(zip_derived_cl23,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk2' @ Y0 )
=> ( ( r @ Y0 )
& ( q @ Y0 ) ) ) )
| ~ '#form3' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl30,plain,
( ~ ( ( irel @ '#sk2' @ '#sk6' )
=> ( ( r @ '#sk6' )
& ( q @ '#sk6' ) ) )
| ~ '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( r @ '#sk6' )
& ( q @ '#sk6' ) )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl48,plain,
( ~ ( r @ '#sk6' )
| ~ ( q @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl94,plain,
( ~ ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3'
| ~ '#form3'
| ~ ( q @ '#sk6' ) ),
inference('sup-',[status(thm)],[zip_derived_cl92,zip_derived_cl48]) ).
thf(zip_derived_cl99,plain,
( ~ ( q @ '#sk6' )
| ~ '#form3'
| ~ ( irel @ '#sk2' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl37,plain,
( ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl101,plain,
( ~ '#form3'
| ~ ( q @ '#sk6' ) ),
inference(clc,[status(thm)],[zip_derived_cl99,zip_derived_cl37]) ).
thf(zip_derived_cl149,plain,
( ~ ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3'
| ~ '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl147,zip_derived_cl101]) ).
thf(zip_derived_cl154,plain,
( ~ '#form3'
| ~ ( irel @ '#sk2' @ '#sk6' ) ),
inference(simplify,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl37_010,plain,
( ( irel @ '#sk2' @ '#sk6' )
| ~ '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl156,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl154,zip_derived_cl37]) ).
thf(zip_derived_cl158,plain,
irel @ '#sk4' @ '#sk9',
inference(demod,[status(thm)],[zip_derived_cl54,zip_derived_cl156]) ).
thf(zip_derived_cl21,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl156_011,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl154,zip_derived_cl37]) ).
thf(zip_derived_cl157,plain,
irel @ '#sk1' @ '#sk4',
inference(demod,[status(thm)],[zip_derived_cl21,zip_derived_cl156]) ).
thf(zip_derived_cl79_012,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( q @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X6 ) ),
inference(clc,[status(thm)],[zip_derived_cl67,zip_derived_cl77]) ).
thf(zip_derived_cl169,plain,
! [X0: $i,X1: $i] :
( ~ ( irel @ '#sk4' @ X0 )
| ( p @ X0 )
| ~ ( irel @ '#sk4' @ X1 )
| ( q @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl157,zip_derived_cl79]) ).
thf(zip_derived_cl178,plain,
! [X0: $i] :
( ( q @ X0 )
| ~ ( irel @ '#sk4' @ X0 )
| ( p @ '#sk9' ) ),
inference('sup-',[status(thm)],[zip_derived_cl158,zip_derived_cl169]) ).
thf(zip_derived_cl55,plain,
( ~ ( p @ '#sk9' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl156_013,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl154,zip_derived_cl37]) ).
thf(zip_derived_cl159,plain,
~ ( p @ '#sk9' ),
inference(demod,[status(thm)],[zip_derived_cl55,zip_derived_cl156]) ).
thf(zip_derived_cl181,plain,
! [X0: $i] :
( ( q @ X0 )
| ~ ( irel @ '#sk4' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl178,zip_derived_cl159]) ).
thf(zip_derived_cl35,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( r @ Y0 ) ) )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl44,plain,
( ~ ( ( irel @ '#sk4' @ '#sk8' )
=> ( r @ '#sk8' ) )
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) )
| '#form3' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl52,plain,
( ( irel @ '#sk4' @ '#sk8' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl59,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl60,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| '#form10' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl68,plain,
( ~ ( ( irel @ '#sk4' @ '#sk11' )
=> ( q @ '#sk11' ) )
| '#form10' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl73,plain,
( ~ ( q @ '#sk11' )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl156_014,plain,
~ '#form3',
inference(clc,[status(thm)],[zip_derived_cl154,zip_derived_cl37]) ).
thf(zip_derived_cl52_015,plain,
( ( irel @ '#sk4' @ '#sk8' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl59_016,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl62,plain,
( ~ '#form10'
| '#form3'
| ( irel @ '#sk4' @ '#sk8' ) ),
inference(renaming,[status(thm)],[zip_derived_cl52,zip_derived_cl59]) ).
thf(zip_derived_cl54_017,plain,
( ( irel @ '#sk4' @ '#sk9' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl21_018,plain,
( ( irel @ '#sk1' @ '#sk4' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl78_019,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( irel @ '#sk1' @ X2 )
| ( r @ X4 )
| ~ ( irel @ X2 @ X4 )
| ( p @ X6 )
| ~ ( irel @ X2 @ X6 ) ),
inference(clc,[status(thm)],[zip_derived_cl64,zip_derived_cl76]) ).
thf(zip_derived_cl80,plain,
! [X0: $i,X1: $i] :
( '#form3'
| ~ ( irel @ '#sk4' @ X0 )
| ( p @ X0 )
| ~ ( irel @ '#sk4' @ X1 )
| ( r @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl21,zip_derived_cl78]) ).
thf(zip_derived_cl112,plain,
! [X0: $i] :
( '#form3'
| ( r @ X0 )
| ~ ( irel @ '#sk4' @ X0 )
| ( p @ '#sk9' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl54,zip_derived_cl80]) ).
thf(zip_derived_cl118,plain,
! [X0: $i] :
( ( p @ '#sk9' )
| ~ ( irel @ '#sk4' @ X0 )
| ( r @ X0 )
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl112]) ).
thf(zip_derived_cl55_020,plain,
( ~ ( p @ '#sk9' )
| '#form3' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl122,plain,
! [X0: $i] :
( '#form3'
| ( r @ X0 )
| ~ ( irel @ '#sk4' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl118,zip_derived_cl55]) ).
thf(zip_derived_cl126,plain,
( '#form3'
| ~ '#form10'
| ( r @ '#sk8' )
| '#form3' ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl122]) ).
thf(zip_derived_cl132,plain,
( ( r @ '#sk8' )
| ~ '#form10'
| '#form3' ),
inference(simplify,[status(thm)],[zip_derived_cl126]) ).
thf(zip_derived_cl53,plain,
( ~ ( r @ '#sk8' )
| '#form3'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl59_021,plain,
( '#form10'
| ~ ( ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( q @ Y0 ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( irel @ '#sk4' @ Y0 )
=> ( p @ Y0 ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
( ~ '#form10'
| '#form3'
| ~ ( r @ '#sk8' ) ),
inference(renaming,[status(thm)],[zip_derived_cl53,zip_derived_cl59]) ).
thf(zip_derived_cl135,plain,
( '#form3'
| ~ '#form10' ),
inference(clc,[status(thm)],[zip_derived_cl132,zip_derived_cl63]) ).
thf(zip_derived_cl162,plain,
~ '#form10',
inference('sup+',[status(thm)],[zip_derived_cl156,zip_derived_cl135]) ).
thf(zip_derived_cl165,plain,
~ ( q @ '#sk11' ),
inference(demod,[status(thm)],[zip_derived_cl73,zip_derived_cl162]) ).
thf(zip_derived_cl183,plain,
~ ( irel @ '#sk4' @ '#sk11' ),
inference('sup-',[status(thm)],[zip_derived_cl181,zip_derived_cl165]) ).
thf(zip_derived_cl72,plain,
( ( irel @ '#sk4' @ '#sk11' )
| '#form10' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl162_022,plain,
~ '#form10',
inference('sup+',[status(thm)],[zip_derived_cl156,zip_derived_cl135]) ).
thf(zip_derived_cl164,plain,
irel @ '#sk4' @ '#sk11',
inference(demod,[status(thm)],[zip_derived_cl72,zip_derived_cl162]) ).
thf(zip_derived_cl185,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl183,zip_derived_cl164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN045^4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.aeFVvPX4zf true
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 21:29:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.19/0.35 % Python version: Python 3.6.8
% 0.19/0.35 % Running in HO mode
% 0.21/0.67 % Total configuration time : 828
% 0.21/0.67 % Estimated wc time : 1656
% 0.21/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.92/0.81 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.43/0.87 % Solved by lams/20_acsne_simpl.sh.
% 1.43/0.87 % done 49 iterations in 0.069s
% 1.43/0.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.43/0.87 % SZS output start Refutation
% See solution above
% 1.43/0.87
% 1.43/0.87
% 1.43/0.87 % Terminating...
% 1.53/1.02 % Runner terminated.
% 1.53/1.04 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------