%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PLA033^7 : TPTP v9.2.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jG0xB1wP6a 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 04:49:14 PM UTC 2025
% Result : Theorem 0.37s 0.97s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 78 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 293 ( 27 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 720 ( 127 ~; 106 |; 0 &; 475 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 6 con; 0-3 aty)
% Number of variables : 179 ( 58 ^; 121 !; 0 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(closed_type,type,
closed: mu > $i > $o ).
thf(combo_type,type,
combo: mu > mu > $i > $o ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(sk__9_type,type,
sk__9: $i > mu ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(h_type,type,
h: mu > $i > $o ).
thf(sk__10_type,type,
sk__10: $i ).
thf(d_type,type,
d: mu ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(sk__11_type,type,
sk__11: $i ).
thf(sk__8_type,type,
sk__8: mu > mu > $i > mu ).
thf(sk__12_type,type,
sk__12: $i ).
thf(o_type,type,
o: mu ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(open_type,type,
open: mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('0',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('1',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('2',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('3',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ) ).
thf('4',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('5',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(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('6',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
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,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind,'5','7']) ).
thf('9',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [V_2: mu] : ( mnot @ ( V_1 @ V_2 ) ) ) ) ) ),
define([status(thm)]) ).
thf(ax5,axiom,
( mvalid
@ ( mexists_ind
@ ^ [V: mu] : ( mbox_s4 @ ( combo @ d @ V ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i] :
~ ! [X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ~ ! [X8: $i] :
( ( combo @ d @ X6 @ X8 )
| ~ ( rel_s4 @ X4 @ X8 ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i] : ( exists_in_world @ ( sk__9 @ X0 ) @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
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('10',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('11',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('12',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'11','7']) ).
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,'11','7']) ).
thf('15',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(con,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [O: mu] : ( mimplies @ ( mbox_s4 @ ( mand @ ( combo @ d @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ d ) ) ) ) ) ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i,X6: $i] :
( ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ( ~ ! [X12: $i] :
( ~ ( ~ ( combo @ d @ X8 @ X12 )
| ~ ( h @ X10 @ X12 ) )
| ~ ( rel_s4 @ X6 @ X12 ) )
| ! [X14: $i] :
( ( open @ d @ X14 )
| ~ ( rel_s4 @ X6 @ X14 ) ) ) ) )
| ~ ( rel_s4 @ X4 @ X6 ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ( ~ ! [X12: $i] :
( ~ ( ~ ( combo @ d @ X8 @ X12 )
| ~ ( h @ X10 @ X12 ) )
| ~ ( rel_s4 @ X6 @ X12 ) )
| ! [X14: $i] :
( ( open @ d @ X14 )
| ~ ( rel_s4 @ X6 @ X14 ) ) ) ) )
| ~ ( rel_s4 @ X4 @ X6 ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl17,plain,
! [X0: mu,X1: mu] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ( rel_s4 @ sk__11 @ sk__12 )
| ~ ( exists_in_world @ X1 @ sk__11 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl55,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ( rel_s4 @ sk__11 @ sk__12 ) ),
inference(condensation,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl56,plain,
rel_s4 @ sk__11 @ sk__12,
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl55]) ).
thf(zip_derived_cl13_001,plain,
! [X0: $i] : ( exists_in_world @ ( sk__9 @ X0 ) @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl15,plain,
rel_s4 @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(existence_of_d_ax,axiom,
! [V: $i] : ( exists_in_world @ d @ V ) ).
thf(zip_derived_cl6,plain,
! [X0: $i] : ( exists_in_world @ d @ X0 ),
inference(cnf,[status(esa)],[existence_of_d_ax]) ).
thf(ax1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] :
( mforall_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [O: mu] : ( mand @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( combo @ S @ V ) @ ( h @ O ) ) ) @ ( mbox_s4 @ ( open @ S ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( closed @ S ) @ ( mand @ ( mnot @ ( combo @ S @ V ) ) @ ( h @ o ) ) ) @ ( mbox_s4 @ ( closed @ S ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: $i] :
( ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ! [X12: mu] :
( ( exists_in_world @ X12 @ X6 )
=> ( ~ ! [X14: $i] :
( ~ ( combo @ X8 @ X10 @ X14 )
| ~ ( h @ X12 @ X14 )
| ~ ( closed @ X8 @ X14 )
| ! [X16: $i] :
( ( open @ X8 @ X16 )
| ~ ( rel_s4 @ X14 @ X16 ) )
| ~ ( rel_s4 @ X6 @ X14 ) )
| ~ ! [X18: $i] :
( ( combo @ X8 @ X10 @ X18 )
| ~ ( h @ o @ X18 )
| ~ ( closed @ X8 @ X18 )
| ! [X20: $i] :
( ( closed @ X8 @ X20 )
| ~ ( rel_s4 @ X18 @ X20 ) )
| ~ ( rel_s4 @ X6 @ X18 ) ) ) ) ) )
| ~ ( rel_s4 @ X4 @ X6 ) ) ).
thf(zip_derived_cl8,plain,
! [X0: mu,X1: $i,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X0 @ X1 )
| ( exists_in_world @ ( sk__8 @ X2 @ X0 @ X1 ) @ X1 )
| ~ ( exists_in_world @ X2 @ X1 )
| ~ ( rel_s4 @ X3 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl154,plain,
! [X0: $i,X1: $i,X2: mu] :
( ~ ( rel_s4 @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X0 )
| ( exists_in_world @ ( sk__8 @ X2 @ d @ X0 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl8]) ).
thf(zip_derived_cl278,plain,
! [X0: mu] :
( ( exists_in_world @ ( sk__8 @ X0 @ d @ sk__11 ) @ sk__11 )
| ~ ( exists_in_world @ X0 @ sk__11 ) ),
inference('sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl154]) ).
thf(zip_derived_cl19,plain,
! [X0: mu,X1: mu,X2: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X2 )
| ( h @ X0 @ X2 )
| ~ ( exists_in_world @ X1 @ sk__11 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl122,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ( h @ X0 @ X1 ) ),
inference(condensation,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl7,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i,X4: mu,X5: $i] :
( ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ( open @ X0 @ X3 )
| ~ ( rel_s4 @ X2 @ X3 )
| ~ ( closed @ X0 @ X2 )
| ~ ( h @ ( sk__8 @ X4 @ X0 @ X1 ) @ X2 )
| ~ ( combo @ X0 @ X4 @ X2 )
| ~ ( exists_in_world @ X4 @ X1 )
| ~ ( rel_s4 @ X5 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl123,plain,
! [X0: $i,X1: $i,X2: mu,X3: mu,X4: $i,X5: $i] :
( ~ ( rel_s4 @ sk__11 @ X0 )
| ~ ( exists_in_world @ ( sk__8 @ X3 @ X2 @ X1 ) @ sk__11 )
| ~ ( rel_s4 @ X4 @ X1 )
| ~ ( exists_in_world @ X3 @ X1 )
| ~ ( combo @ X2 @ X3 @ X0 )
| ~ ( closed @ X2 @ X0 )
| ~ ( rel_s4 @ X0 @ X5 )
| ( open @ X2 @ X5 )
| ~ ( rel_s4 @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl122,zip_derived_cl7]) ).
thf(zip_derived_cl310,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( exists_in_world @ d @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ( open @ d @ X2 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( closed @ d @ X1 )
| ~ ( combo @ d @ X0 @ X1 )
| ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ X3 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl278,zip_derived_cl123]) ).
thf(zip_derived_cl6_002,plain,
! [X0: $i] : ( exists_in_world @ d @ X0 ),
inference(cnf,[status(esa)],[existence_of_d_ax]) ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('16',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('17',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_4,axiom,
! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(ax2,axiom,
mvalid @ ( mbox_s4 @ ( closed @ d ) ) ).
thf(zf_stmt_5,axiom,
! [X4: $i,X6: $i] :
( ( closed @ d @ X6 )
| ~ ( rel_s4 @ X4 @ X6 ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i] :
( ( closed @ d @ X0 )
| ~ ( rel_s4 @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl21,plain,
! [X0: $i] : ( closed @ d @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl10]) ).
thf(zip_derived_cl320,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ( open @ d @ X2 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( combo @ d @ X0 @ X1 )
| ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ X3 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl310,zip_derived_cl6,zip_derived_cl21]) ).
thf(zip_derived_cl321,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ sk__11 )
| ~ ( combo @ d @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ( open @ d @ X2 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ~ ( exists_in_world @ X0 @ sk__11 ) ),
inference(simplify,[status(thm)],[zip_derived_cl320]) ).
thf(zip_derived_cl18,plain,
! [X0: mu,X1: mu,X2: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X2 )
| ( combo @ d @ X1 @ X2 )
| ~ ( exists_in_world @ X1 @ sk__11 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl125,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ( combo @ d @ X0 @ X1 ) ),
inference(condensation,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl434,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ( open @ d @ X2 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( rel_s4 @ X3 @ sk__11 ) ),
inference(clc,[status(thm)],[zip_derived_cl321,zip_derived_cl125]) ).
thf(zip_derived_cl1_003,plain,
! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl6_004,plain,
! [X0: $i] : ( exists_in_world @ d @ X0 ),
inference(cnf,[status(esa)],[existence_of_d_ax]) ).
thf(ax4,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] : ( mnot @ ( mand @ ( open @ S ) @ ( closed @ S ) ) ) ) ) ) ).
thf(zf_stmt_6,axiom,
! [X4: $i,X6: $i] :
( ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ( ~ ( open @ X8 @ X6 )
| ~ ( closed @ X8 @ X6 ) ) )
| ~ ( rel_s4 @ X4 @ X6 ) ) ).
thf(zip_derived_cl12,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( exists_in_world @ X0 @ X1 )
| ~ ( open @ X0 @ X1 )
| ~ ( closed @ X0 @ X1 )
| ~ ( rel_s4 @ X2 @ X1 ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl39,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X1 @ X0 )
| ~ ( closed @ d @ X0 )
| ~ ( open @ d @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl6,zip_derived_cl12]) ).
thf(zip_derived_cl21_005,plain,
! [X0: $i] : ( closed @ d @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl10]) ).
thf(zip_derived_cl47,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X1 @ X0 )
| ~ ( open @ d @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl39,zip_derived_cl21]) ).
thf(zip_derived_cl51,plain,
! [X0: $i] :
~ ( open @ d @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl1,zip_derived_cl47]) ).
thf(zip_derived_cl435,plain,
! [X0: mu,X1: $i,X2: $i,X3: $i] :
( ~ ( rel_s4 @ X3 @ sk__11 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( rel_s4 @ sk__11 @ X1 )
| ~ ( exists_in_world @ X0 @ sk__11 ) ),
inference(clc,[status(thm)],[zip_derived_cl434,zip_derived_cl51]) ).
thf(zip_derived_cl440,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl435]) ).
thf(zip_derived_cl1_006,plain,
! [X0: $i] : ( rel_s4 @ X0 @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl448,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ sk__11 )
| ~ ( rel_s4 @ sk__11 @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl1]) ).
thf(zip_derived_cl456,plain,
! [X0: $i] :
~ ( rel_s4 @ sk__11 @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl13,zip_derived_cl448]) ).
thf(zip_derived_cl499,plain,
$false,
inference('sup-',[status(thm)],[zip_derived_cl56,zip_derived_cl456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : PLA033^7 : TPTP v9.2.0. Released v5.5.0.
% 0.08/0.16 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.jG0xB1wP6a true
% 0.14/0.39 % Computer : n009.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Wed Oct 1 11:06:08 EDT 2025
% 0.14/0.39 % CPUTime :
% 0.14/0.39 % Running portfolio for 300 s
% 0.14/0.39 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.39 % Number of cores: 8
% 0.22/0.39 % Python version: Python 3.6.8
% 0.22/0.40 % Running in HO mode
% 0.36/0.72 % Total configuration time : 828
% 0.36/0.72 % Estimated wc time : 1656
% 0.36/0.72 % Estimated cpu time (8 cpus) : 207.0
% 0.36/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.36/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.36/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.36/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.36/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.36/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.36/0.81 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.36/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.36/0.86 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.37/0.97 % Solved by lams/40_c.s.sh.
% 0.37/0.97 % done 162 iterations in 0.175s
% 0.37/0.97 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.37/0.97 % SZS output start Refutation
% See solution above
% 0.37/0.98
% 0.37/0.98
% 0.37/0.98 % Terminating...
% 0.38/1.01 % Runner terminated.
% 0.38/1.02 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------