%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI043^2 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.I7ufyw6HIy true
% Computer : n027.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 : Thu Oct 2 04:49:08 PM UTC 2025
% Result : Theorem 1.44s 0.88s
% Output : Refutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 31
% Syntax : Number of formulae : 79 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 347 ( 36 equ; 51 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 702 ( 86 ~; 22 |; 12 &; 452 @)
% ( 16 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 106 ( 106 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 18 usr; 8 con; 0-3 aty)
% ( 53 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 186 ( 143 ^; 38 !; 5 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mdia_type,type,
mdia: ( $i > $o ) > $i > $o ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(mexists_eiw_ind_type,type,
mexists_eiw_ind: ( mu > $i > $o ) > $i > $o ).
thf(eiw_ind_type,type,
eiw_ind: $i > mu > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mbox_generic_type,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk40_type',type,
'#sk40': $i ).
thf(mdia_generic_type,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(p_type,type,
p: ( mu > $i > $o ) > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mforall_indset_type,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mbox_type,type,
mbox: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mforall_eiw_ind_type,type,
mforall_eiw_ind: ( mu > $i > $o ) > $i > $o ).
thf('#form65_type',type,
'#form65': $o ).
thf('#sk2_type',type,
'#sk2': mu > $i > $o ).
thf(mexists_eiw_ind,axiom,
( mexists_eiw_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
thf(mforall_eiw_ind,axiom,
( mforall_eiw_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( eiw_ind @ W @ X )
=> ( Phi @ X @ W ) ) ) ) ).
thf('0',plain,
( mforall_eiw_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( eiw_ind @ W @ X )
=> ( Phi @ X @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_eiw_ind]) ).
thf('1',plain,
( mforall_eiw_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] :
( ( eiw_ind @ V_2 @ X4 )
=> ( V_1 @ X4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('2',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('3',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('4',plain,
( mexists_eiw_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_eiw_ind,'1','3']) ).
thf('5',plain,
( mexists_eiw_ind
= ( ^ [V_1: mu > $i > $o] :
( mnot
@ ( mforall_eiw_ind
@ ^ [V_2: mu] : ( mnot @ ( V_1 @ V_2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('6',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('7',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mdia,axiom,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(mdia_generic,axiom,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ) ).
thf('8',plain,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_generic]) ).
thf('9',plain,
( mdia_generic
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
? [X4: $i] :
( ( V_2 @ X4 )
& ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('10',plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mdia,'9']) ).
thf('11',plain,
( mdia
= ( mdia_generic @ rel ) ),
define([status(thm)]) ).
thf(mforall_indset,axiom,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
thf('12',plain,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_indset]) ).
thf('13',plain,
( mforall_indset
= ( ^ [V_1: ( mu > $i > $o ) > $i > $o,V_2: $i] :
! [X4: mu > $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ) ).
thf('14',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies]) ).
thf('15',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
=> ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(possible_instantiation_of_the_positive_variable_domain,conjecture,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( p @ Phi )
@ ( mdia
@ ( mexists_eiw_ind
@ ^ [X: mu] : ( Phi @ X ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: mu > $i > $o] :
( ( p @ X6 @ X4 )
=> ? [X8: $i] :
( ( rel @ X4 @ X8 )
& ~ ! [X10: mu] :
( ( eiw_ind @ X8 @ X10 )
=> ~ ( X6 @ X10 @ X8 ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i,X6: mu > $i > $o] :
( ( p @ X6 @ X4 )
=> ? [X8: $i] :
( ( rel @ X4 @ X8 )
& ~ ! [X10: mu] :
( ( eiw_ind @ X8 @ X10 )
=> ~ ( X6 @ X10 @ X8 ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( p @ Y1 @ Y0 )
=> ( ??
@ ^ [Y2: $i] :
( ( rel @ Y0 @ Y2 )
& ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( eiw_ind @ Y2 @ Y3 )
=> ( (~) @ ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl4,plain,
~ ( !!
@ ^ [Y0: mu > $i > $o] :
( ( p @ Y0 @ '#sk1' )
=> ( ??
@ ^ [Y1: $i] :
( ( rel @ '#sk1' @ Y1 )
& ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( (~) @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
~ ( ( p @ '#sk2' @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
p @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(mbox,axiom,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(mbox_generic,axiom,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ) ).
thf('16',plain,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_generic]) ).
thf('17',plain,
( mbox_generic
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
! [X4: $i] :
( ( V_2 @ X4 )
| ~ ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('18',plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mbox,'17']) ).
thf('19',plain,
( mbox
= ( mbox_generic @ rel ) ),
define([status(thm)]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ) ).
thf('20',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv]) ).
thf('21',plain,
( mequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
<=> ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(axii,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies
@ ( mbox
@ ( mforall_eiw_ind
@ ^ [X: mu] : ( mequiv @ ( Phi @ X ) @ ( Psi @ X ) ) ) )
@ ( mequiv @ ( p @ Phi ) @ ( p @ Psi ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: mu > $i > $o,X8: mu > $i > $o] :
( ! [X10: $i] :
( ~ ( rel @ X4 @ X10 )
| ! [X12: mu] :
( ( eiw_ind @ X10 @ X12 )
=> ( ( X6 @ X12 @ X10 )
<=> ( X8 @ X12 @ X10 ) ) ) )
=> ( ( p @ X6 @ X4 )
<=> ( p @ X8 @ X4 ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu > $i > $o] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( eiw_ind @ Y3 @ Y4 )
=> ( ( Y1 @ Y4 @ Y3 )
<=> ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( p @ Y1 @ Y0 )
<=> ( p @ Y2 @ Y0 ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel @ X2 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( eiw_ind @ Y2 @ Y3 )
=> ( ( Y0 @ Y3 @ Y2 )
<=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( p @ Y0 @ X2 )
<=> ( p @ Y1 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: mu > $i > $o] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( ( X4 @ Y2 @ Y1 )
<=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( p @ X4 @ X2 )
<=> ( p @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl22,plain,
! [X0: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ X0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( $false
<=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( p
@ ^ [Y1: mu,Y2: $i] : $false
@ X0 )
<=> ( p @ Y0 @ X0 ) ) ) ),
inference('ho.refine.early.bird',[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl24,plain,
! [X0: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ X0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( eiw_ind @ Y1 @ Y2 )
=> ( (~) @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( p
@ ^ [Y1: mu,Y2: $i] : $false
@ X0 )
<=> ( p @ Y0 @ X0 ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( X2 @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X0 )
<=> ( p @ X2 @ X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(ax16,axiom,
( mvalid
@ ( mnot
@ ( p
@ ^ [X: mu,W: $i] : ( X != X ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i] :
~ ( p
@ ^ [V_1: mu,V_2: $i] : ( V_1 != V_1 )
@ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( (~)
@ ( p
@ ^ [Y1: mu,Y2: $i] : ( Y1 != Y1 )
@ Y0 ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: $i] :
( (~)
@ ( p
@ ^ [Y1: mu,Y2: $i] : $false
@ Y0 ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
~ ( p
@ ^ [Y0: mu,Y1: $i] : $false
@ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( X2 @ Y1 @ Y0 ) ) ) ) ) )
=> ( $false
<=> ( p @ X2 @ X0 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl25,zip_derived_cl13]) ).
thf(zip_derived_cl31,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( X2 @ Y1 @ Y0 ) ) ) ) ) )
=> ( (~) @ ( p @ X2 @ X0 ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl32,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ '#sk1' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) )
=> ( (~) @ $true ) ),
inference('sup+',[status(thm)],[zip_derived_cl6,zip_derived_cl31]) ).
thf(zip_derived_cl35,plain,
( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ '#sk1' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl36,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ '#sk1' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl39,plain,
~ ( ( (~) @ ( rel @ '#sk1' @ '#sk40' ) )
| ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl39_001,plain,
~ ( ( (~) @ ( rel @ '#sk1' @ '#sk40' ) )
| ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl42,plain,
rel @ '#sk1' @ '#sk40',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl49,plain,
~ ( ( (~) @ $true )
| ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl39,zip_derived_cl42]) ).
thf(zip_derived_cl50,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl50_002,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl61,plain,
( '#form65'
| ~ ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl63,plain,
~ '#form65',
inference(renaming,[status(thm)],[zip_derived_cl50,zip_derived_cl61]) ).
thf(zip_derived_cl42_003,plain,
rel @ '#sk1' @ '#sk40',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl5_004,plain,
~ ( ( p @ '#sk2' @ '#sk1' )
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6_005,plain,
p @ '#sk2' @ '#sk1',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl8,plain,
~ ( $true
=> ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl6]) ).
thf(zip_derived_cl9,plain,
~ ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( eiw_ind @ Y0 @ Y1 )
=> ( (~) @ ( '#sk2' @ Y1 @ Y0 ) ) ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
~ ( ( rel @ '#sk1' @ X2 )
& ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ X2 @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ X2 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl15,plain,
! [X2: $i] :
( ~ ( rel @ '#sk1' @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ X2 @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl52,plain,
( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl15]) ).
thf(zip_derived_cl52_006,plain,
( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl42,zip_derived_cl15]) ).
thf(zip_derived_cl79,plain,
( ~ '#form65'
| ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl61_007,plain,
( '#form65'
| ~ ( !!
@ ^ [Y0: mu] :
( ( eiw_ind @ '#sk40' @ Y0 )
=> ( (~) @ ( '#sk2' @ Y0 @ '#sk40' ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl81,plain,
'#form65',
inference(renaming,[status(thm)],[zip_derived_cl52,zip_derived_cl79,zip_derived_cl61]) ).
thf(zip_derived_cl83,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : PHI043^2 : TPTP v9.2.0. Released v7.5.0.
% 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.I7ufyw6HIy true
% 0.11/0.31 % Computer : n027.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Wed Oct 1 16:57:08 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % Running portfolio for 300 s
% 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Number of cores: 8
% 0.11/0.32 % Python version: Python 3.6.8
% 0.11/0.32 % Running in HO mode
% 0.16/0.62 % Total configuration time : 828
% 0.16/0.62 % Estimated wc time : 1656
% 0.16/0.62 % Estimated cpu time (8 cpus) : 207.0
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.92/0.70 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.92/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.35/0.70 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.35/0.70 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.35/0.70 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.35/0.72 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.35/0.74 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.44/0.76 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.44/0.88 % Solved by lams/35_full_unif.sh.
% 1.44/0.88 % done 33 iterations in 0.076s
% 1.44/0.88 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.44/0.88 % SZS output start Refutation
% See solution above
% 1.44/0.88
% 1.44/0.88
% 1.44/0.88 % Terminating...
% 1.57/0.93 % Runner terminated.
% 1.73/0.94 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------