%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO568^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AtxOPDFzf9 true
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 2 05:07:56 PM UTC 2025
% Result : Theorem 0.55s 0.83s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 27
% Syntax : Number of formulae : 88 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 442 ( 30 equ; 82 cnn)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 1009 ( 157 ~; 134 |; 9 &; 643 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 17 usr; 8 con; 0-3 aty)
% ( 49 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 176 ( 104 ^; 72 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(f_type,type,
f: mu > $i > $o ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $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(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a_type,type,
a: mu ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('0',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('1',plain,
( mreflexive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i] : ( V_1 @ X4 @ X4 ) ) ),
define([status(thm)]) ).
thf(a1,axiom,
mreflexive @ rel_s4 ).
thf(zf_stmt_0,axiom,
! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('2',plain,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('3',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s4 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('4',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('5',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ) ).
thf('6',plain,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).
thf('7',plain,
( mforall_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] :
( ( exists_in_world @ X4 @ V_2 )
=> ( V_1 @ X4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('8',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('9',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
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('10',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('11',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('12',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'9','11']) ).
thf('13',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('14',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'9','11']) ).
thf('15',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('16',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'13','15','9','11']) ).
thf('17',plain,
( mequiv
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mand @ ( mimplies @ V_1 @ V_2 ) @ ( mimplies @ V_2 @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(con,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X: mu] : ( mor @ ( mbox_s4 @ ( f @ X ) ) @ ( mbox_s4 @ ( mnot @ ( f @ X ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i] :
( ! [X12: $i] :
( ~ ( rel_s4 @ X4 @ X12 )
| ~ ( ~ ( ! [X16: $i] :
( ~ ( rel_s4 @ X12 @ X16 )
| ( f @ a @ X16 ) )
| ~ ( f @ a @ X12 ) )
| ~ ( ( f @ a @ X12 )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X12 @ X14 )
| ( f @ a @ X14 ) ) ) ) )
| ~ ! [X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ( ! [X10: $i] :
( ~ ( rel_s4 @ X4 @ X10 )
| ~ ( f @ X6 @ X10 ) )
| ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ( f @ X6 @ X8 ) ) ) ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i] :
( ! [X12: $i] :
( ~ ( rel_s4 @ X4 @ X12 )
| ~ ( ~ ( ! [X16: $i] :
( ~ ( rel_s4 @ X12 @ X16 )
| ( f @ a @ X16 ) )
| ~ ( f @ a @ X12 ) )
| ~ ( ( f @ a @ X12 )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X12 @ X14 )
| ( f @ a @ X14 ) ) ) ) )
| ~ ! [X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ( ! [X10: $i] :
( ~ ( rel_s4 @ X4 @ X10 )
| ~ ( f @ X6 @ X10 ) )
| ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ( f @ X6 @ X8 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( f @ a @ Y2 ) ) )
| ( (~) @ ( f @ a @ Y1 ) ) ) )
| ( (~)
@ ( ( f @ a @ Y1 )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( f @ a @ Y2 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~) @ ( f @ Y1 @ Y2 ) ) ) )
| ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( f @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl30,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( f @ a @ Y1 ) ) )
| ( (~) @ ( f @ a @ Y0 ) ) ) )
| ( (~)
@ ( ( f @ a @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( f @ a @ Y1 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y1 ) )
| ( (~) @ ( f @ Y0 @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y1 ) )
| ( f @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl31,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( f @ a @ Y1 ) ) )
| ( (~) @ ( f @ a @ Y0 ) ) ) )
| ( (~)
@ ( ( f @ a @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( f @ a @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl33,plain,
~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk3' ) )
| ( (~)
@ ( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ( (~) @ ( f @ a @ '#sk3' ) ) ) )
| ( (~)
@ ( ( f @ a @ '#sk3' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl36,plain,
( ( (~)
@ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ( (~) @ ( f @ a @ '#sk3' ) ) ) )
| ( (~)
@ ( ( f @ a @ '#sk3' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl38,plain,
( ~ ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ( (~) @ ( f @ a @ '#sk3' ) ) )
| ~ ( ( f @ a @ '#sk3' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl41,plain,
( ( f @ a @ '#sk3' )
| ~ ( ( f @ a @ '#sk3' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl46,plain,
( ( f @ a @ '#sk3' )
| ~ ( $false
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl47,plain,
( ( f @ a @ '#sk3' )
| ~ ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl48,plain,
( ( f @ a @ '#sk3' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ X2 ) )
| ( f @ a @ X2 )
| ( f @ a @ '#sk3' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk3' @ X2 )
| ( f @ a @ X2 )
| ( f @ a @ '#sk3' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl64,plain,
( ( f @ a @ '#sk3' )
| ( f @ a @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl7,zip_derived_cl53]) ).
thf(zip_derived_cl66,plain,
f @ a @ '#sk3',
inference(simplify,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl32,plain,
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y1 ) )
| ( (~) @ ( f @ Y0 @ Y1 ) ) ) )
| ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y1 ) )
| ( f @ Y0 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl34,plain,
! [X2: mu] :
( ( exists_in_world @ X2 @ '#sk2' )
=> ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( (~) @ ( f @ X2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( f @ X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl37,plain,
! [X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk2' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( (~) @ ( f @ X2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( f @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl39,plain,
! [X2: mu] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( (~) @ ( f @ X2 @ Y0 ) ) ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( f @ X2 @ Y0 ) ) )
| ~ ( exists_in_world @ X2 @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl42,plain,
! [X2: mu,X4: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X4 ) )
| ( (~) @ ( f @ X2 @ X4 ) )
| ~ ( exists_in_world @ X2 @ '#sk2' )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( f @ X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl50,plain,
! [X2: mu,X4: $i] :
( ~ ( rel_s4 @ '#sk2' @ X4 )
| ~ ( f @ X2 @ X4 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( f @ X2 @ Y0 ) ) )
| ~ ( exists_in_world @ X2 @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl54,plain,
! [X2: mu,X4: $i,X6: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X6 ) )
| ( f @ X2 @ X6 )
| ~ ( exists_in_world @ X2 @ '#sk2' )
| ~ ( f @ X2 @ X4 )
| ~ ( rel_s4 @ '#sk2' @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl55,plain,
! [X2: mu,X4: $i,X6: $i] :
( ~ ( rel_s4 @ '#sk2' @ X6 )
| ( f @ X2 @ X6 )
| ~ ( rel_s4 @ '#sk2' @ X4 )
| ~ ( f @ X2 @ X4 )
| ~ ( exists_in_world @ X2 @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl82,plain,
! [X0: $i] :
( ~ ( exists_in_world @ a @ '#sk2' )
| ~ ( rel_s4 @ '#sk2' @ '#sk3' )
| ( f @ a @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl55]) ).
thf(existence_of_a_ax,axiom,
! [V: $i] : ( exists_in_world @ a @ V ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] : ( exists_in_world @ a @ Y0 ) ),
inference(cnf,[status(esa)],[existence_of_a_ax]) ).
thf(zip_derived_cl6,plain,
! [X2: $i] : ( exists_in_world @ a @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl35,plain,
rel_s4 @ '#sk2' @ '#sk3',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl87,plain,
! [X0: $i] :
( ( f @ a @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl82,zip_derived_cl6,zip_derived_cl35]) ).
thf(zip_derived_cl40,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ~ ( ( f @ a @ '#sk3' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl43,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ~ ( ( f @ a @ '#sk3' )
| ( (~) @ $true ) ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl44,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( f @ a @ Y0 ) ) )
| ~ ( f @ a @ '#sk3' ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl45,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk3' @ '#sk4' ) )
| ( f @ a @ '#sk4' ) )
| ~ ( f @ a @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl52,plain,
( ~ ( f @ a @ '#sk4' )
| ~ ( f @ a @ '#sk3' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl66_001,plain,
f @ a @ '#sk3',
inference(simplify,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl69,plain,
~ ( f @ a @ '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl52,zip_derived_cl66]) ).
thf(zip_derived_cl90,plain,
~ ( rel_s4 @ '#sk2' @ '#sk4' ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl69]) ).
thf(zip_derived_cl35_002,plain,
rel_s4 @ '#sk2' @ '#sk3',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl51,plain,
( ( rel_s4 @ '#sk3' @ '#sk4' )
| ~ ( f @ a @ '#sk3' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl66_003,plain,
f @ a @ '#sk3',
inference(simplify,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl68,plain,
rel_s4 @ '#sk3' @ '#sk4',
inference(demod,[status(thm)],[zip_derived_cl51,zip_derived_cl66]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('18',plain,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).
thf('19',plain,
( mtransitive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(a2,axiom,
mtransitive @ rel_s4 ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rel_s4 @ X6 @ X8 )
& ( rel_s4 @ X4 @ X6 ) )
=> ( rel_s4 @ X4 @ X8 ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl10,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ X2 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X4 @ Y0 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( rel_s4 @ X2 @ X4 )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl71,plain,
! [X0: $i] :
( ( rel_s4 @ X0 @ '#sk4' )
| ~ ( rel_s4 @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl68,zip_derived_cl14]) ).
thf(zip_derived_cl100,plain,
rel_s4 @ '#sk2' @ '#sk4',
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl71]) ).
thf(zip_derived_cl104,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl90,zip_derived_cl100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO568^7 : TPTP v9.2.0. Released v5.5.0.
% 0.03/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.AtxOPDFzf9 true
% 0.13/0.33 % Computer : n009.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 : Wed Oct 1 18:05:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.33 % Running portfolio for 300 s
% 0.13/0.33 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Number of cores: 8
% 0.13/0.34 % Python version: Python 3.6.8
% 0.13/0.34 % Running in HO mode
% 0.54/0.67 % Total configuration time : 828
% 0.54/0.67 % Estimated wc time : 1656
% 0.54/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.54/0.74 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.54/0.75 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.55/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.55/0.80 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 0.55/0.83 % Solved by lams/35_full_unif4.sh.
% 0.55/0.83 % done 39 iterations in 0.041s
% 0.55/0.83 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.55/0.83 % SZS output start Refutation
% See solution above
% 0.55/0.83
% 0.55/0.83
% 0.55/0.83 % Terminating...
% 0.56/0.86 % Runner terminated.
% 1.76/0.87 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------