TSTP Solution File: SET576^7 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g4Tn4RxGuP true
% Computer : n029.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 Aug 31 16:14:39 EDT 2023
% Result : Theorem 1.58s 0.87s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 39
% Syntax : Number of formulae : 98 ( 38 unt; 17 typ; 0 def)
% Number of atoms : 517 ( 24 equ; 116 cnn)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 1391 ( 207 ~; 136 |; 0 &; 944 @)
% ( 0 <=>; 62 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 6 con; 0-3 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 174 ( 98 ^; 76 !; 0 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf('#sk2_type',type,
'#sk2': $i ).
thf(intersect_type,type,
intersect: mu > mu > $i > $o ).
thf('#sk5_type',type,
'#sk5': $i > mu > mu > 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(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(member_type,type,
member: mu > mu > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': mu ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': mu ).
thf(disjoint_type,type,
disjoint: 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(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('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(mnot,axiom,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ) ).
thf('4',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('5',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('6',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind,'3','5']) ).
thf('7',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [V_2: mu] : ( mnot @ ( V_1 @ 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('10',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'9','5']) ).
thf('11',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('12',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'9','5']) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf('14',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mand @ ( mimplies @ Phi @ Psi ) @ ( mimplies @ Psi @ Phi ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv,'11','13','9','5']) ).
thf('15',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(intersect_defn,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mequiv @ ( intersect @ B @ C )
@ ( mexists_ind
@ ^ [D: mu] : ( mand @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( ~ ( ( intersect @ 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 ) ) )
| ~ ( intersect @ X6 @ X8 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl4,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl74,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ Y0 @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl75,plain,
! [X2: $i,X4: mu] :
( ( exists_in_world @ X4 @ X2 )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl74]) ).
thf(zip_derived_cl76,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl77,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( ( exists_in_world @ X6 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ X4 @ X6 @ X2 ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl78,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( exists_in_world @ X6 @ X2 )
| ~ ( ( (~)
@ ( ( intersect @ 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 ) ) ) ) ) )
| ( (~) @ ( intersect @ X4 @ X6 @ X2 ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl80,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) ) )
| ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl78]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( ( (~) @ ( member @ Y0 @ X6 @ X2 ) )
| ( (~) @ ( member @ Y0 @ X4 @ X2 ) ) ) ) )
| ~ ( intersect @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( ( exists_in_world @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X2 )
=> ( ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 ) )
| ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( intersect @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 ) )
| ( (~) @ ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 ) ) )
| ~ ( intersect @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( intersect @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).
thf(prove_th17,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] :
( mimplies
@ ( mforall_ind
@ ^ [D: mu] : ( mimplies @ ( member @ D @ B ) @ ( mnot @ ( member @ D @ C ) ) ) )
@ ( disjoint @ B @ C ) ) ) ) ) ).
thf(zf_stmt_1,conjecture,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ( ( disjoint @ X6 @ X8 @ X4 )
| ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ~ ( member @ X10 @ X8 @ X4 )
| ~ ( member @ X10 @ X6 @ X4 ) ) ) ) ) ) ).
thf(zf_stmt_2,negated_conjecture,
~ ! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ( ( disjoint @ X6 @ X8 @ X4 )
| ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X4 )
=> ( ~ ( member @ X10 @ X8 @ X4 )
| ~ ( member @ X10 @ X6 @ X4 ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ( disjoint @ Y1 @ Y2 @ Y0 )
| ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( (~) @ ( member @ Y3 @ Y2 @ Y0 ) )
| ( (~) @ ( member @ Y3 @ Y1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl50,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( ( disjoint @ Y0 @ Y1 @ '#sk2' )
| ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk2' )
=> ( ( (~) @ ( member @ Y2 @ Y1 @ '#sk2' ) )
| ( (~) @ ( member @ Y2 @ Y0 @ '#sk2' ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl51,plain,
~ ( ( exists_in_world @ '#sk3' @ '#sk2' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( disjoint @ '#sk3' @ Y0 @ '#sk2' )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( ( (~) @ ( member @ Y1 @ Y0 @ '#sk2' ) )
| ( (~) @ ( member @ Y1 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl53,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( disjoint @ '#sk3' @ Y0 @ '#sk2' )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk2' )
=> ( ( (~) @ ( member @ Y1 @ Y0 @ '#sk2' ) )
| ( (~) @ ( member @ Y1 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl54,plain,
~ ( ( exists_in_world @ '#sk4' @ '#sk2' )
=> ( ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl56,plain,
~ ( ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl58,plain,
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk2' )
=> ( ( (~) @ ( member @ Y0 @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( member @ Y0 @ '#sk3' @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl59,plain,
! [X2: mu] :
( ( exists_in_world @ X2 @ '#sk2' )
=> ( ( (~) @ ( member @ X2 @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( member @ X2 @ '#sk3' @ '#sk2' ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl60,plain,
! [X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk2' )
| ( (~) @ ( member @ X2 @ '#sk4' @ '#sk2' ) )
| ( (~) @ ( member @ X2 @ '#sk3' @ '#sk2' ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl61,plain,
! [X2: mu] :
( ~ ( member @ X2 @ '#sk4' @ '#sk2' )
| ~ ( member @ X2 @ '#sk3' @ '#sk2' )
| ~ ( exists_in_world @ X2 @ '#sk2' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl111,plain,
! [X0: mu] :
( ~ ( intersect @ X0 @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk2' )
| ~ ( member @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk3' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl61]) ).
thf(zip_derived_cl55,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl113,plain,
! [X0: mu] :
( ~ ( intersect @ X0 @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ X0 @ '#sk2' )
| ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk2' )
| ~ ( member @ ( '#sk5' @ '#sk2' @ X0 @ '#sk4' ) @ '#sk3' @ '#sk2' ) ),
inference(demod,[status(thm)],[zip_derived_cl111,zip_derived_cl55]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( member @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X4 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( intersect @ X4 @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl131,plain,
( ~ ( exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2' )
| ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( intersect @ '#sk3' @ '#sk4' @ '#sk2' )
| ~ ( intersect @ '#sk3' @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ~ ( exists_in_world @ '#sk3' @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl113,zip_derived_cl90]) ).
thf(disjoint_defn,axiom,
( mvalid
@ ( mforall_ind
@ ^ [B: mu] :
( mforall_ind
@ ^ [C: mu] : ( mequiv @ ( disjoint @ B @ C ) @ ( mnot @ ( intersect @ B @ C ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ! [X8: mu] :
( ( exists_in_world @ X8 @ X4 )
=> ~ ( ~ ( ( disjoint @ X6 @ X8 @ X4 )
| ( intersect @ X6 @ X8 @ X4 ) )
| ~ ( ~ ( intersect @ X6 @ X8 @ X4 )
| ~ ( disjoint @ X6 @ X8 @ X4 ) ) ) ) ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ Y1 @ Y2 @ Y0 )
| ( intersect @ Y1 @ Y2 @ Y0 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ Y1 @ Y2 @ Y0 ) )
| ( (~) @ ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl41,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ Y0 @ Y1 @ X2 )
| ( intersect @ Y0 @ Y1 @ X2 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ Y0 @ Y1 @ X2 ) )
| ( (~) @ ( disjoint @ Y0 @ Y1 @ X2 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: mu] :
( ( exists_in_world @ X4 @ X2 )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ X4 @ Y0 @ X2 )
| ( intersect @ X4 @ Y0 @ X2 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) )
| ( (~) @ ( disjoint @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl43,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ X4 @ Y0 @ X2 )
| ( intersect @ X4 @ Y0 @ X2 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ X4 @ Y0 @ X2 ) )
| ( (~) @ ( disjoint @ X4 @ Y0 @ X2 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl44,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( ( exists_in_world @ X6 @ X2 )
=> ( (~)
@ ( ( (~)
@ ( ( disjoint @ X4 @ X6 @ X2 )
| ( intersect @ X4 @ X6 @ X2 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
| ( (~) @ ( disjoint @ X4 @ X6 @ X2 ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl45,plain,
! [X2: $i,X4: mu,X6: mu] :
( ~ ( exists_in_world @ X6 @ X2 )
| ~ ( ( (~)
@ ( ( disjoint @ X4 @ X6 @ X2 )
| ( intersect @ X4 @ X6 @ X2 ) ) )
| ( (~)
@ ( ( (~) @ ( intersect @ X4 @ X6 @ X2 ) )
| ( (~) @ ( disjoint @ X4 @ X6 @ X2 ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl46,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( disjoint @ X4 @ X6 @ X2 )
| ( intersect @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl48,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( disjoint @ X4 @ X6 @ X2 )
| ( intersect @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl57,plain,
~ ( disjoint @ '#sk3' @ '#sk4' @ '#sk2' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl63,plain,
( ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ( intersect @ '#sk3' @ '#sk4' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl48,zip_derived_cl57]) ).
thf(zip_derived_cl52,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl55_001,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl66,plain,
intersect @ '#sk3' @ '#sk4' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: mu,X6: mu] :
( ( exists_in_world @ ( '#sk5' @ X2 @ X4 @ X6 ) @ X2 )
| ~ ( intersect @ X4 @ X6 @ X2 )
| ~ ( exists_in_world @ X6 @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl91,plain,
( ~ ( exists_in_world @ '#sk3' @ '#sk2' )
| ~ ( exists_in_world @ '#sk4' @ '#sk2' )
| ( exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl66,zip_derived_cl86]) ).
thf(zip_derived_cl52_002,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl55_003,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl93,plain,
exists_in_world @ ( '#sk5' @ '#sk2' @ '#sk3' @ '#sk4' ) @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl91,zip_derived_cl52,zip_derived_cl55]) ).
thf(zip_derived_cl52_004,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl66_005,plain,
intersect @ '#sk3' @ '#sk4' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).
thf(zip_derived_cl66_006,plain,
intersect @ '#sk3' @ '#sk4' @ '#sk2',
inference(demod,[status(thm)],[zip_derived_cl63,zip_derived_cl52,zip_derived_cl55]) ).
thf(zip_derived_cl55_007,plain,
exists_in_world @ '#sk4' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl52_008,plain,
exists_in_world @ '#sk3' @ '#sk2',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl137,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl131,zip_derived_cl93,zip_derived_cl52,zip_derived_cl66,zip_derived_cl66,zip_derived_cl55,zip_derived_cl52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET576^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.g4Tn4RxGuP true
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 13:09:24 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.68 % Total configuration time : 828
% 0.22/0.68 % Estimated wc time : 1656
% 0.22/0.68 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.82 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.83 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.58/0.87 % Solved by lams/35_full_unif4.sh.
% 1.58/0.87 % done 29 iterations in 0.070s
% 1.58/0.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.58/0.87 % SZS output start Refutation
% See solution above
% 1.58/0.87
% 1.58/0.87
% 1.58/0.87 % Terminating...
% 2.29/0.96 % Runner terminated.
% 2.29/0.97 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------