%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.APtYv42kUD true
% Computer : n025.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 05:08:28 PM UTC 2025
% Result : Theorem 28.09s 5.08s
% Output : Refutation 28.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 28
% Syntax : Number of formulae : 102 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 492 ( 33 equ; 11 cnn)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1183 ( 81 ~; 71 |; 0 &; 762 @)
% ( 0 <=>; 139 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 88 ( 88 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 10 con; 0-3 aty)
% ( 130 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 320 ( 189 ^; 131 !; 0 ?; 320 :)
% Comments :
%------------------------------------------------------------------------------
thf(individuals_type,type,
individuals: $tType ).
thf(cs4_atom_type,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf('#sk9_type',type,
'#sk9': ( $i > $o ) > $i > $i ).
thf(cs4_impl_type,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(reli_type,type,
reli: $i > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i ).
thf('#sk7_type',type,
'#sk7': individuals ).
thf('#sk6_type',type,
'#sk6': $i ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(relr_type,type,
relr: $i > $i > $o ).
thf(mimpl_type,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(cs4_all_type,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(mall_type,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(cs4_box_type,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': individuals > $i > $o ).
thf(cs4_valid_type,type,
cs4_valid: ( $i > $o ) > $o ).
thf(mbox_type,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(cs4_valid_def,axiom,
( cs4_valid
= ( ^ [A: $i > $o] : ( mvalid @ A ) ) ) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ) ).
thf('0',plain,
( mvalid
= ( ^ [P: $i > $o] :
! [W: $i] : ( P @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('1',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf('2',plain,
( cs4_valid
= ( ^ [A: $i > $o] : ( mvalid @ A ) ) ),
inference(simplify_rw_rule,[status(thm)],[cs4_valid_def,'1']) ).
thf('3',plain,
( cs4_valid
= ( ^ [V_1: $i > $o] : ( mvalid @ V_1 ) ) ),
define([status(thm)]) ).
thf(cs4_box,axiom,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ) ).
thf(mbox,axiom,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ) ).
thf('4',plain,
( mbox
= ( ^ [R: $i > $i > $o,P: $i > $o,X: $i] :
! [Y: $i] :
( ( R @ X @ Y )
=> ( P @ Y ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox]) ).
thf('5',plain,
( mbox
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
! [X4: $i] :
( ( V_1 @ V_3 @ X4 )
=> ( V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('6',plain,
( cs4_box
= ( ^ [A: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cs4_box,'5']) ).
thf('7',plain,
( cs4_box
= ( ^ [V_1: $i > $o] : ( mbox @ reli @ ( mbox @ relr @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(cs4_all,axiom,
( cs4_all
= ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ) ).
thf(mall,axiom,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ) ).
thf('8',plain,
( mall
= ( ^ [P: individuals > $i > $o,W: $i] :
! [X: individuals] : ( P @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mall]) ).
thf('9',plain,
( mall
= ( ^ [V_1: individuals > $i > $o,V_2: $i] :
! [X4: individuals] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( cs4_all
= ( ^ [A: individuals > $i > $o] : ( mbox @ reli @ ( mall @ A ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cs4_all,'9','5']) ).
thf('11',plain,
( cs4_all
= ( ^ [V_1: individuals > $i > $o] : ( mbox @ reli @ ( mall @ V_1 ) ) ) ),
define([status(thm)]) ).
thf(cs4_impl,axiom,
( cs4_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ) ).
thf(mimpl,axiom,
( mimpl
= ( ^ [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('12',plain,
( mor
= ( ^ [X: $i > $o,Y: $i > $o,U: $i] :
( ( X @ U )
| ( Y @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('13',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('14',plain,
( mnot
= ( ^ [X: $i > $o,U: $i] :
~ ( X @ U ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('15',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('16',plain,
( mimpl
= ( ^ [U: $i > $o,V: $i > $o] : ( mor @ ( mnot @ U ) @ V ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimpl,'13','15']) ).
thf('17',plain,
( mimpl
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf('18',plain,
( cs4_impl
= ( ^ [A: $i > $o,B: $i > $o] : ( mbox @ reli @ ( mimpl @ A @ B ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[cs4_impl,'5','17','13','15']) ).
thf('19',plain,
( cs4_impl
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mbox @ reli @ ( mimpl @ V_1 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(cs4_atom,axiom,
( cs4_atom
= ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ) ).
thf('20',plain,
( cs4_atom
= ( ^ [P: $i > $o] : ( mbox @ reli @ P ) ) ),
inference(simplify_rw_rule,[status(thm)],[cs4_atom,'5']) ).
thf('21',plain,
( cs4_atom
= ( ^ [V_1: $i > $o] : ( mbox @ reli @ V_1 ) ) ),
define([status(thm)]) ).
thf(cs4_barcan,conjecture,
! [A: individuals > $i > $o] :
( cs4_valid
@ ( cs4_impl
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_box @ ( cs4_atom @ ( A @ I ) ) ) )
@ ( cs4_box
@ ( cs4_all
@ ^ [I: individuals] : ( cs4_atom @ ( A @ I ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: individuals > $i > $o,X6: $i,X8: $i] :
( ( reli @ X6 @ X8 )
=> ( ! [X20: $i] :
( ( reli @ X8 @ X20 )
=> ! [X22: $i] :
( ( relr @ X20 @ X22 )
=> ! [X24: $i] :
( ( reli @ X22 @ X24 )
=> ! [X26: individuals,X28: $i] :
( ( reli @ X24 @ X28 )
=> ( X4 @ X26 @ X28 ) ) ) ) )
| ~ ! [X10: $i] :
( ( reli @ X8 @ X10 )
=> ! [X12: individuals,X14: $i] :
( ( reli @ X10 @ X14 )
=> ! [X16: $i] :
( ( relr @ X14 @ X16 )
=> ! [X18: $i] :
( ( reli @ X16 @ X18 )
=> ( X4 @ X12 @ X18 ) ) ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: individuals > $i > $o,X6: $i,X8: $i] :
( ( reli @ X6 @ X8 )
=> ( ! [X20: $i] :
( ( reli @ X8 @ X20 )
=> ! [X22: $i] :
( ( relr @ X20 @ X22 )
=> ! [X24: $i] :
( ( reli @ X22 @ X24 )
=> ! [X26: individuals,X28: $i] :
( ( reli @ X24 @ X28 )
=> ( X4 @ X26 @ X28 ) ) ) ) )
| ~ ! [X10: $i] :
( ( reli @ X8 @ X10 )
=> ! [X12: individuals,X14: $i] :
( ( reli @ X10 @ X14 )
=> ! [X16: $i] :
( ( relr @ X14 @ X16 )
=> ! [X18: $i] :
( ( reli @ X16 @ X18 )
=> ( X4 @ X12 @ X18 ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: individuals > $i > $o] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !!
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( !!
@ ^ [Y6: individuals] :
( !!
@ ^ [Y7: $i] :
( ( reli @ Y5 @ Y7 )
=> ( Y0 @ Y6 @ Y7 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: individuals] :
( !!
@ ^ [Y5: $i] :
( ( reli @ Y3 @ Y5 )
=> ( !!
@ ^ [Y6: $i] :
( ( relr @ Y5 @ Y6 )
=> ( !!
@ ^ [Y7: $i] :
( ( reli @ Y6 @ Y7 )
=> ( Y0 @ Y4 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( !!
@ ^ [Y5: individuals] :
( !!
@ ^ [Y6: $i] :
( ( reli @ Y4 @ Y6 )
=> ( '#sk1' @ Y5 @ Y6 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: individuals] :
( !!
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( !!
@ ^ [Y5: $i] :
( ( relr @ Y4 @ Y5 )
=> ( !!
@ ^ [Y6: $i] :
( ( reli @ Y5 @ Y6 )
=> ( '#sk1' @ Y3 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk2' @ Y0 )
=> ( ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: individuals] :
( !!
@ ^ [Y5: $i] :
( ( reli @ Y3 @ Y5 )
=> ( '#sk1' @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: individuals] :
( !!
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( relr @ Y3 @ Y4 )
=> ( !!
@ ^ [Y5: $i] :
( ( reli @ Y4 @ Y5 )
=> ( '#sk1' @ Y2 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
~ ( ( reli @ '#sk2' @ '#sk3' )
=> ( ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: individuals] :
( !!
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: individuals] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( '#sk1' @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl10,plain,
~ ( ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: individuals] :
( !!
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: individuals] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( '#sk1' @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl11,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: individuals] :
( !!
@ ^ [Y4: $i] :
( ( reli @ Y2 @ Y4 )
=> ( '#sk1' @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl13,plain,
~ ( ( reli @ '#sk3' @ '#sk4' )
=> ( !!
@ ^ [Y0: $i] :
( ( relr @ '#sk4' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: individuals] :
( !!
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl16,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( relr @ '#sk4' @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: individuals] :
( !!
@ ^ [Y3: $i] :
( ( reli @ Y1 @ Y3 )
=> ( '#sk1' @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl18,plain,
~ ( ( relr @ '#sk4' @ '#sk5' )
=> ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk5' @ Y0 )
=> ( !!
@ ^ [Y1: individuals] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl21,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk5' @ Y0 )
=> ( !!
@ ^ [Y1: individuals] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( '#sk1' @ Y1 @ Y2 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl23,plain,
~ ( ( reli @ '#sk5' @ '#sk6' )
=> ( !!
@ ^ [Y0: individuals] :
( !!
@ ^ [Y1: $i] :
( ( reli @ '#sk6' @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl26,plain,
~ ( !!
@ ^ [Y0: individuals] :
( !!
@ ^ [Y1: $i] :
( ( reli @ '#sk6' @ Y1 )
=> ( '#sk1' @ Y0 @ Y1 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl28,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk6' @ Y0 )
=> ( '#sk1' @ '#sk7' @ Y0 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl30,plain,
~ ( ( reli @ '#sk6' @ '#sk8' )
=> ( '#sk1' @ '#sk7' @ '#sk8' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl33,plain,
~ ( '#sk1' @ '#sk7' @ '#sk8' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl20,plain,
relr @ '#sk4' @ '#sk5',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl18]) ).
thf(refl_axiom_i,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ A ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i > $o,X6: $i] :
( ( X4 @ X6 )
| ~ ! [X8: $i] :
( ( reli @ X6 @ X8 )
=> ( X4 @ X8 ) ) ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl39,plain,
! [X2: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl40,plain,
! [X2: $i > $o,X4: $i] :
( ( X2 @ X4 )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: $i > $o,X4: $i] :
( ( X2 @ X4 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl42,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( ( reli @ X4 @ ( '#sk9' @ X2 @ X4 ) )
=> ( X2 @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl43,plain,
! [X2: $i > $o,X4: $i] :
( ( reli @ X4 @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl44,plain,
! [X2: $i > $o,X4: $i] :
( ~ ( X2 @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl50,plain,
! [X0: $i] :
( ( reli @ X0 @ X0 )
| ( reli @ X0 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl44]) ).
thf(zip_derived_cl51,plain,
! [X0: $i] : ( reli @ X0 @ X0 ),
inference(simplify,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl25,plain,
reli @ '#sk5' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32,plain,
reli @ '#sk6' @ '#sk8',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(trans_axiom_i,axiom,
! [A: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ reli @ A ) @ ( mbox @ reli @ ( mbox @ reli @ A ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i > $o,X6: $i] :
( ! [X10: $i] :
( ( reli @ X6 @ X10 )
=> ! [X12: $i] :
( ( reli @ X10 @ X12 )
=> ( X4 @ X12 ) ) )
| ~ ! [X8: $i] :
( ( reli @ X6 @ X8 )
=> ( X4 @ X8 ) ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i > $o] :
( !!
@ ^ [Y1: $i] :
( ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl82,plain,
! [X2: $i > $o] :
( !!
@ ^ [Y0: $i] :
( ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl83,plain,
! [X2: $i > $o,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X2: $i > $o,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl85,plain,
! [X2: $i > $o,X4: $i,X6: $i] :
( ( ( reli @ X4 @ X6 )
=> ( !!
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl86,plain,
! [X2: $i > $o,X4: $i,X6: $i] :
( ~ ( reli @ X4 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( reli @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl87,plain,
! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
( ( ( reli @ X6 @ X8 )
=> ( X2 @ X8 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ~ ( reli @ X4 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl88,plain,
! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
( ~ ( reli @ X6 @ X8 )
| ( X2 @ X8 )
| ~ ( reli @ X4 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( reli @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl89,plain,
! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
( ~ ( ( reli @ X4 @ ( '#sk9' @ X2 @ X4 ) )
=> ( X2 @ ( '#sk9' @ X2 @ X4 ) ) )
| ~ ( reli @ X4 @ X6 )
| ( X2 @ X8 )
| ~ ( reli @ X6 @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl91,plain,
! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
( ~ ( X2 @ ( '#sk9' @ X2 @ X4 ) )
| ~ ( reli @ X6 @ X8 )
| ( X2 @ X8 )
| ~ ( reli @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl119,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( reli @ X0 @ '#sk6' )
| ( X1 @ '#sk8' )
| ~ ( X1 @ ( '#sk9' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl91]) ).
thf(zip_derived_cl773,plain,
! [X0: $i > $o] :
( ~ ( X0 @ ( '#sk9' @ X0 @ '#sk5' ) )
| ( X0 @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl119]) ).
thf(zip_derived_cl25_001,plain,
reli @ '#sk5' @ '#sk6',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl32_002,plain,
reli @ '#sk6' @ '#sk8',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl90,plain,
! [X2: $i > $o,X4: $i,X6: $i,X8: $i] :
( ( reli @ X4 @ ( '#sk9' @ X2 @ X4 ) )
| ~ ( reli @ X6 @ X8 )
| ( X2 @ X8 )
| ~ ( reli @ X4 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl97,plain,
! [X0: $i,X1: $i > $o] :
( ~ ( reli @ X0 @ '#sk6' )
| ( X1 @ '#sk8' )
| ( reli @ X0 @ ( '#sk9' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl90]) ).
thf(zip_derived_cl315,plain,
! [X0: $i > $o] :
( ( reli @ '#sk5' @ ( '#sk9' @ X0 @ '#sk5' ) )
| ( X0 @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl25,zip_derived_cl97]) ).
thf(zip_derived_cl2340,plain,
( ( reli @ '#sk5' @ '#sk8' )
| ( reli @ '#sk5' @ '#sk8' ) ),
inference('sup+',[status(thm)],[zip_derived_cl773,zip_derived_cl315]) ).
thf(zip_derived_cl2341,plain,
reli @ '#sk5' @ '#sk8',
inference(simplify,[status(thm)],[zip_derived_cl2340]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: $i] :
( ( reli @ '#sk3' @ Y0 )
=> ( !!
@ ^ [Y1: individuals] :
( !!
@ ^ [Y2: $i] :
( ( reli @ Y0 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( relr @ Y2 @ Y3 )
=> ( !!
@ ^ [Y4: $i] :
( ( reli @ Y3 @ Y4 )
=> ( '#sk1' @ Y1 @ Y4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl14,plain,
! [X2: $i] :
( ( reli @ '#sk3' @ X2 )
=> ( !!
@ ^ [Y0: individuals] :
( !!
@ ^ [Y1: $i] :
( ( reli @ X2 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( '#sk1' @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl17,plain,
! [X2: $i] :
( ~ ( reli @ '#sk3' @ X2 )
| ( !!
@ ^ [Y0: individuals] :
( !!
@ ^ [Y1: $i] :
( ( reli @ X2 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( relr @ Y1 @ Y2 )
=> ( !!
@ ^ [Y3: $i] :
( ( reli @ Y2 @ Y3 )
=> ( '#sk1' @ Y0 @ Y3 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: individuals] :
( ( !!
@ ^ [Y0: $i] :
( ( reli @ X2 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( relr @ Y0 @ Y1 )
=> ( !!
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( '#sk1' @ X4 @ Y2 ) ) ) ) ) ) )
| ~ ( reli @ '#sk3' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: individuals,X6: $i] :
( ( ( reli @ X2 @ X6 )
=> ( !!
@ ^ [Y0: $i] :
( ( relr @ X6 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( '#sk1' @ X4 @ Y1 ) ) ) ) ) )
| ~ ( reli @ '#sk3' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: individuals,X6: $i] :
( ~ ( reli @ X2 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( relr @ X6 @ Y0 )
=> ( !!
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( '#sk1' @ X4 @ Y1 ) ) ) ) )
| ~ ( reli @ '#sk3' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: individuals,X6: $i,X8: $i] :
( ( ( relr @ X6 @ X8 )
=> ( !!
@ ^ [Y0: $i] :
( ( reli @ X8 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) ) )
| ~ ( reli @ '#sk3' @ X2 )
| ~ ( reli @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: individuals,X6: $i,X8: $i] :
( ~ ( relr @ X6 @ X8 )
| ( !!
@ ^ [Y0: $i] :
( ( reli @ X8 @ Y0 )
=> ( '#sk1' @ X4 @ Y0 ) ) )
| ~ ( reli @ X2 @ X6 )
| ~ ( reli @ '#sk3' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: individuals,X6: $i,X8: $i,X10: $i] :
( ( ( reli @ X8 @ X10 )
=> ( '#sk1' @ X4 @ X10 ) )
| ~ ( reli @ '#sk3' @ X2 )
| ~ ( reli @ X2 @ X6 )
| ~ ( relr @ X6 @ X8 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: individuals,X6: $i,X8: $i,X10: $i] :
( ~ ( reli @ X8 @ X10 )
| ( '#sk1' @ X4 @ X10 )
| ~ ( relr @ X6 @ X8 )
| ~ ( reli @ X2 @ X6 )
| ~ ( reli @ '#sk3' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl2444,plain,
! [X0: $i,X1: $i,X2: individuals] :
( ~ ( reli @ '#sk3' @ X0 )
| ~ ( reli @ X0 @ X1 )
| ~ ( relr @ X1 @ '#sk5' )
| ( '#sk1' @ X2 @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2341,zip_derived_cl34]) ).
thf(zip_derived_cl2739,plain,
! [X0: individuals,X1: $i] :
( ( '#sk1' @ X0 @ '#sk8' )
| ~ ( relr @ X1 @ '#sk5' )
| ~ ( reli @ '#sk3' @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl2444]) ).
thf(zip_derived_cl2748,plain,
! [X0: individuals] :
( ~ ( reli @ '#sk3' @ '#sk4' )
| ( '#sk1' @ X0 @ '#sk8' ) ),
inference('sup-',[status(thm)],[zip_derived_cl20,zip_derived_cl2739]) ).
thf(zip_derived_cl15,plain,
reli @ '#sk3' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl2749,plain,
! [X0: individuals] : ( '#sk1' @ X0 @ '#sk8' ),
inference(demod,[status(thm)],[zip_derived_cl2748,zip_derived_cl15]) ).
thf(zip_derived_cl3061,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl2749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.19 % Problem : SYO886^9 : TPTP v9.2.0. Released v3.7.0.
% 0.10/0.20 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.APtYv42kUD true
% 0.11/0.39 % Computer : n025.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8042.1875MB
% 0.11/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Oct 1 18:10:53 EDT 2025
% 0.11/0.39 % CPUTime :
% 0.11/0.39 % Running portfolio for 300 s
% 0.11/0.39 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.40 % Number of cores: 8
% 0.11/0.40 % Python version: Python 3.6.8
% 0.11/0.40 % Running in HO mode
% 0.37/0.68 % Total configuration time : 828
% 0.37/0.68 % Estimated wc time : 1656
% 0.37/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.37/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.38/0.99 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.38/1.00 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.38/1.00 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.38/1.01 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.38/1.03 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.38/1.04 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.38/1.06 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.57/1.23 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.68/1.32 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 1.68/1.35 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 30s
% 1.68/1.36 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 30s
% 28.09/5.08 % Solved by lams/15_lifting3.sh.
% 28.09/5.08 % done 266 iterations in 3.617s
% 28.09/5.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 28.09/5.08 % SZS output start Refutation
% See solution above
% 28.09/5.08
% 28.09/5.08
% 28.09/5.08 % Terminating...
% 28.61/5.20 % Runner terminated.
% 28.61/5.21 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------