%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET027^7 : 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.apu68xEMd3 true
% Computer : n005.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 04:51:14 PM UTC 2025
% Result : Theorem 0.64s 0.88s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 81 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 446 ( 21 equ; 67 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1294 ( 167 ~; 147 |; 0 &; 890 @)
% ( 0 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 7 con; 0-3 aty)
% ( 36 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 165 ( 84 ^; 81 !; 0 ?; 165 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(member_type,type,
member: mu > mu > $i > $o ).
thf('#sk4_type',type,
'#sk4': mu ).
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(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk6_type',type,
'#sk6': $i > mu > mu > mu ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk5_type',type,
'#sk5': mu ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': mu ).
thf(subset_type,type,
subset: mu > mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('0',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ 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(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ) ).
thf('2',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('3',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(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('4',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
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
= ( ^ [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,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
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(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('10',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'5','7']) ).
thf('11',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(prove_transitivity_of_subset,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ D ) ) @ ( subset @ B @ D ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ( subset @ X6 @ X10 @ X4 )
| ~ ( subset @ X6 @ X8 @ X4 )
| ~ ( subset @ X8 @ X10 @ X4 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ( subset @ X6 @ X10 @ X4 )
| ~ ( subset @ X6 @ X8 @ X4 )
| ~ ( subset @ X8 @ X10 @ X4 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl6,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( subset @ Y1 @ Y3 @ Y0 )
| ( (~) @ ( subset @ Y1 @ Y2 @ Y0 ) )
| ( (~) @ ( subset @ Y2 @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl23,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk2' )
=> ( ( subset @ Y0 @ Y2 @ '#sk2' )
| ( (~) @ ( subset @ Y0 @ Y1 @ '#sk2' ) )
| ( (~) @ ( subset @ Y1 @ Y2 @ '#sk2' ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl24,plain,
~ ( ( exists_in_world @ '#sk3' @ '#sk2' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( ( subset @ '#sk3' @ Y1 @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ Y0 @ '#sk2' ) )
| ( (~) @ ( subset @ Y0 @ Y1 @ '#sk2' ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl26,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( ( subset @ '#sk3' @ Y1 @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ Y0 @ '#sk2' ) )
| ( (~) @ ( subset @ Y0 @ Y1 @ '#sk2' ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl27,plain,
~ ( ( exists_in_world @ '#sk4' @ '#sk2' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( subset @ '#sk3' @ Y0 @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( subset @ '#sk4' @ Y0 @ '#sk2' ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl29,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( subset @ '#sk3' @ Y0 @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( subset @ '#sk4' @ Y0 @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl30,plain,
~ ( ( exists_in_world @ '#sk5' @ '#sk2' )
=> ( ( subset @ '#sk3' @ '#sk5' @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( subset @ '#sk4' @ '#sk5' @ '#sk2' ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl32,plain,
~ ( ( subset @ '#sk3' @ '#sk5' @ '#sk2' )
| ( (~) @ ( subset @ '#sk3' @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( subset @ '#sk4' @ '#sk5' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl33,plain,
~ ( subset @ '#sk3' @ '#sk5' @ '#sk2' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ) ).
thf('12',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'9','11','5','7']) ).
thf('13',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(subset_defn,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( subset @ B @ C )
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( ~ ( ( subset @ X6 @ X8 @ X4 )
| ~ ! [X12: mu] :
( ( exists_in_world @ X12 @ X4 )
=> ( ( member @ X12 @ X8 @ X4 )
| ~ ( member @ X12 @ X6 @ X4 ) ) ) )
| ~ ( ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ( member @ X10 @ X8 @ X4 )
| ~ ( member @ X10 @ X6 @ X4 ) ) )
| ~ ( subset @ X6 @ X8 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( subset @ Y1 @ Y2 @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( member @ Y3 @ Y2 @ Y0 )
| ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) )
| ( (~) @ ( subset @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl36,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( subset @ Y0 @ Y1 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ( member @ Y2 @ Y1 @ X2 )
| ( (~) @ ( member @ Y2 @ Y0 @ X2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X2 )
=> ( ( member @ Y2 @ Y1 @ X2 )
| ( (~) @ ( member @ Y2 @ Y0 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ Y0 @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: mu] :
( ( exists_in_world @ X4 @ X2 )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( subset @ X4 @ Y0 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ( member @ Y1 @ Y0 @ X2 )
| ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ( member @ Y1 @ Y0 @ X2 )
| ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( subset @ X4 @ Y0 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ( member @ Y1 @ Y0 @ X2 )
| ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( ( member @ Y1 @ Y0 @ X2 )
| ( (~) @ ( member @ Y1 @ X4 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( ( exists_in_world @ X6 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( subset @ X4 @ X6 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ X4 @ X6 @ X2 ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( exists_in_world @ X6 @ X2 )
| ~ ( ( (~)
@ ( ( subset @ X4 @ X6 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) ) ) )
| ( (~)
@ ( ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ X4 @ X6 @ X2 ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( subset @ X4 @ X6 @ X2 )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( subset @ X4 @ X6 @ X2 )
| ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( ( exists_in_world @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X6 @ X2 )
| ( (~) @ ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ( subset @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl47,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( exists_in_world @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X2 )
| ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X6 @ X2 )
| ( (~) @ ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) )
| ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl50,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ( subset @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl51,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( member @ ( '#sk6' @ X2 @ X4 @ X6 ) @ X4 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ( subset @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl34,plain,
subset @ '#sk3' @ '#sk4' @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ( (~) @ ( subset @ X4 @ X6 @ X2 ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( member @ Y0 @ X6 @ X2 )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ~ ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: mu,X6: mu,X8: mu] :
( ( ( exists_in_world @ X8 @ X2 )
=> ( ( member @ X8 @ X6 @ X2 )
| ( (~) @ ( member @ X8 @ X4 @ X2 ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( subset @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl49,plain,
! [X2: $i,X4: mu,X6: mu,X8: mu] :
( ~ ( exists_in_world @ X8 @ X2 )
| ( member @ X8 @ X6 @ X2 )
| ( (~) @ ( member @ X8 @ X4 @ X2 ) )
| ~ ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl52,plain,
! [X2: $i,X4: mu,X6: mu,X8: mu] :
( ( member @ X8 @ X6 @ X2 )
| ~ ( member @ X8 @ X4 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X8 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl64,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( member @ X0 @ '#sk3' @ '#sk2' )
| ( member @ X0 @ '#sk4' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl34,zip_derived_cl52]) ).
thf(zip_derived_cl28,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl25,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl70,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( member @ X0 @ '#sk3' @ '#sk2' )
| ( member @ X0 @ '#sk4' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl64,zip_derived_cl28,zip_derived_cl25]) ).
thf(zip_derived_cl77,plain,
! [X0: mu] :
( ( subset @ '#sk3' @ X0 @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ( member @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl51,zip_derived_cl70]) ).
thf(zip_derived_cl25_001,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl86,plain,
! [X0: mu] :
( ( subset @ '#sk3' @ X0 @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ( member @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl77,zip_derived_cl25]) ).
thf(zip_derived_cl35,plain,
subset @ '#sk4' @ '#sk5' @ '#sk2',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl52_002,plain,
! [X2: $i,X4: mu,X6: mu,X8: mu] :
( ( member @ X8 @ X6 @ X2 )
| ~ ( member @ X8 @ X4 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( subset @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X8 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl63,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ '#sk5' @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ~ ( member @ X0 @ '#sk4' @ '#sk2' )
| ( member @ X0 @ '#sk5' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl35,zip_derived_cl52]) ).
thf(zip_derived_cl31,plain,
exists_in_world @ '#sk5' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl28_003,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl69,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( member @ X0 @ '#sk4' @ '#sk2' )
| ( member @ X0 @ '#sk5' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl31,zip_derived_cl28]) ).
thf(zip_derived_cl104,plain,
! [X0: mu] :
( ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ( subset @ '#sk3' @ X0 @ '#sk2' )
| ( member @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk5' @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl69]) ).
thf(zip_derived_cl113,plain,
! [X0: mu] :
( ( member @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk5' @ '#sk2' )
| ( subset @ '#sk3' @ X0 @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ X0 ) @ '#sk2' ) ),
inference(simplify,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl120,plain,
( ( subset @ '#sk3' @ '#sk5' @ '#sk2' )
| ~ ( exists_in_world @ '#sk5' @ '#sk2' )
| ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ '#sk5' ) @ '#sk2' )
| ~ ( exists_in_world @ '#sk5' @ '#sk2' )
| ( subset @ '#sk3' @ '#sk5' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl50,zip_derived_cl113]) ).
thf(zip_derived_cl33_004,plain,
~ ( subset @ '#sk3' @ '#sk5' @ '#sk2' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl31_005,plain,
exists_in_world @ '#sk5' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl25_006,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl31_007,plain,
exists_in_world @ '#sk5' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl33_008,plain,
~ ( subset @ '#sk3' @ '#sk5' @ '#sk2' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl123,plain,
~ ( exists_in_world @ ( '#sk6' @ '#sk2' @ '#sk3' @ '#sk5' ) @ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl120,zip_derived_cl33,zip_derived_cl31,zip_derived_cl25,zip_derived_cl31,zip_derived_cl33]) ).
thf(zip_derived_cl128,plain,
( ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( exists_in_world @ '#sk5' @ '#sk2' )
| ( subset @ '#sk3' @ '#sk5' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl47,zip_derived_cl123]) ).
thf(zip_derived_cl25_009,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl31_010,plain,
exists_in_world @ '#sk5' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl131,plain,
subset @ '#sk3' @ '#sk5' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl128,zip_derived_cl25,zip_derived_cl31]) ).
thf(zip_derived_cl135,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl33,zip_derived_cl131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET027^7 : TPTP v9.2.0. Released v5.5.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.apu68xEMd3 true
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 1 13:16:53 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.37 % Python version: Python 3.6.8
% 0.15/0.37 % Running in HO mode
% 0.57/0.66 % Total configuration time : 828
% 0.57/0.66 % Estimated wc time : 1656
% 0.57/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.62/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.62/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.62/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.62/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.62/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.62/0.79 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.62/0.83 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.62/0.85 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 0.64/0.88 % Solved by lams/30_sp5.sh.
% 0.64/0.88 % done 29 iterations in 0.062s
% 0.64/0.88 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 0.64/0.88 % SZS output start Refutation
% See solution above
% 0.64/0.88
% 0.64/0.88
% 0.64/0.88 % Terminating...
% 0.71/0.98 % Runner terminated.
% 0.71/0.99 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------