TSTP Solution File: PLA032^7 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PLA032^7 : 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.lzY2jXvp4F true
% Computer : n007.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 13:05:20 EDT 2023
% Result : Theorem 1.55s 0.84s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 47
% Syntax : Number of formulae : 108 ( 39 unt; 20 typ; 0 def)
% Number of atoms : 488 ( 27 equ; 89 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 1139 ( 178 ~; 128 |; 6 &; 728 @)
% ( 0 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 6 con; 0-3 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 210 ( 110 ^; 100 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(defused_type,type,
defused: mu > $i > $o ).
thf('#sk6_type',type,
'#sk6': $i > mu ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf(mreflexive_type,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk7_type',type,
'#sk7': $i > mu > mu ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(bomb_type,type,
bomb: mu > $i > $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk5_type',type,
'#sk5': mu ).
thf(h_type,type,
h: 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(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
@ ( mforall_ind
@ ^ [X: mu] :
( mexists_ind
@ ^ [D: mu] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ( ( defused @ X8 @ X6 )
| ~ ( bomb @ X8 @ X6 )
| ~ ( h @ X10 @ X6 ) ) ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ( ( defused @ X8 @ X6 )
| ~ ( bomb @ X8 @ X6 )
| ~ ( h @ X10 @ X6 ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl7,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( (~)
@ ( ( defused @ Y2 @ Y1 )
| ( (~) @ ( bomb @ Y2 @ Y1 ) )
| ( (~) @ ( h @ Y3 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl41,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk3' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( ( defused @ Y1 @ Y0 )
| ( (~) @ ( bomb @ Y1 @ Y0 ) )
| ( (~) @ ( h @ Y2 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl42,plain,
~ ( ( (~) @ ( rel_s4 @ '#sk3' @ '#sk4' ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk4' )
=> ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk4' )
=> ( (~)
@ ( ( defused @ Y0 @ '#sk4' )
| ( (~) @ ( bomb @ Y0 @ '#sk4' ) )
| ( (~) @ ( h @ Y1 @ '#sk4' ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl43,plain,
rel_s4 @ '#sk3' @ '#sk4',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
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_2,axiom,
! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(ax3,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mexists_ind
@ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ D ) ) @ ( defused @ X ) ) ) ) ) ) ) ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ~ ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ~ ! [X12: $i] :
( ~ ( rel_s4 @ X6 @ X12 )
| ( defused @ X8 @ X12 )
| ~ ( bomb @ X8 @ X12 )
| ~ ( h @ X10 @ X12 ) ) ) ) ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y4 ) )
| ( defused @ Y2 @ Y4 )
| ( (~) @ ( bomb @ Y2 @ Y4 ) )
| ( (~) @ ( h @ Y3 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl82,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y3 ) )
| ( defused @ Y1 @ Y3 )
| ( (~) @ ( bomb @ Y1 @ Y3 ) )
| ( (~) @ ( h @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y2 ) )
| ( defused @ Y0 @ Y2 )
| ( (~) @ ( bomb @ Y0 @ Y2 ) )
| ( (~) @ ( h @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ X2 @ X4 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y2 ) )
| ( defused @ Y0 @ Y2 )
| ( (~) @ ( bomb @ Y0 @ Y2 ) )
| ( (~) @ ( h @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i,X6: mu] :
( ( ( exists_in_world @ X6 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( defused @ X6 @ Y1 )
| ( (~) @ ( bomb @ X6 @ Y1 ) )
| ( (~) @ ( h @ Y0 @ Y1 ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i,X6: mu] :
( ~ ( exists_in_world @ X6 @ X4 )
| ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( defused @ X6 @ Y1 )
| ( (~) @ ( bomb @ X6 @ Y1 ) )
| ( (~) @ ( h @ Y0 @ Y1 ) ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i,X6: mu] :
( ~ ( ( exists_in_world @ ( '#sk7' @ X4 @ X6 ) @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( defused @ X6 @ Y0 )
| ( (~) @ ( bomb @ X6 @ Y0 ) )
| ( (~) @ ( h @ ( '#sk7' @ X4 @ X6 ) @ Y0 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl88,plain,
! [X2: $i,X4: $i,X6: mu] :
( ( exists_in_world @ ( '#sk7' @ X4 @ X6 ) @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl93,plain,
! [X0: $i,X1: mu] :
( ~ ( exists_in_world @ X1 @ X0 )
| ( exists_in_world @ ( '#sk7' @ X0 @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl8,zip_derived_cl88]) ).
thf(zip_derived_cl44,plain,
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk4' )
=> ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk4' )
=> ( (~)
@ ( ( defused @ Y0 @ '#sk4' )
| ( (~) @ ( bomb @ Y0 @ '#sk4' ) )
| ( (~) @ ( h @ Y1 @ '#sk4' ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl45,plain,
~ ( ( exists_in_world @ '#sk5' @ '#sk4' )
=> ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk4' )
=> ( (~)
@ ( ( defused @ '#sk5' @ '#sk4' )
| ( (~) @ ( bomb @ '#sk5' @ '#sk4' ) )
| ( (~) @ ( h @ Y0 @ '#sk4' ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl47,plain,
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk4' )
=> ( (~)
@ ( ( defused @ '#sk5' @ '#sk4' )
| ( (~) @ ( bomb @ '#sk5' @ '#sk4' ) )
| ( (~) @ ( h @ Y0 @ '#sk4' ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl48,plain,
! [X2: mu] :
( ( exists_in_world @ X2 @ '#sk4' )
=> ( (~)
@ ( ( defused @ '#sk5' @ '#sk4' )
| ( (~) @ ( bomb @ '#sk5' @ '#sk4' ) )
| ( (~) @ ( h @ X2 @ '#sk4' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk4' )
| ~ ( ( defused @ '#sk5' @ '#sk4' )
| ( (~) @ ( bomb @ '#sk5' @ '#sk4' ) )
| ( (~) @ ( h @ X2 @ '#sk4' ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl52,plain,
! [X2: mu] :
( ( h @ X2 @ '#sk4' )
| ~ ( exists_in_world @ X2 @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: $i,X6: mu] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( defused @ X6 @ Y0 )
| ( (~) @ ( bomb @ X6 @ Y0 ) )
| ( (~) @ ( h @ ( '#sk7' @ X4 @ X6 ) @ Y0 ) ) ) )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i,X6: mu,X8: $i] :
( ( (~) @ ( rel_s4 @ X4 @ X8 ) )
| ( defused @ X6 @ X8 )
| ( (~) @ ( bomb @ X6 @ X8 ) )
| ( (~) @ ( h @ ( '#sk7' @ X4 @ X6 ) @ X8 ) )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl91,plain,
! [X2: $i,X4: $i,X6: mu,X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ( defused @ X6 @ X8 )
| ~ ( bomb @ X6 @ X8 )
| ~ ( h @ ( '#sk7' @ X4 @ X6 ) @ X8 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl106,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( exists_in_world @ ( '#sk7' @ X1 @ X0 ) @ '#sk4' )
| ~ ( rel_s4 @ X2 @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( bomb @ X0 @ '#sk4' )
| ( defused @ X0 @ '#sk4' )
| ~ ( rel_s4 @ X1 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl52,zip_derived_cl91]) ).
thf(zip_derived_cl138,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ '#sk4' )
| ~ ( rel_s4 @ '#sk4' @ '#sk4' )
| ( defused @ X0 @ '#sk4' )
| ~ ( bomb @ X0 @ '#sk4' )
| ~ ( exists_in_world @ X0 @ '#sk4' )
| ~ ( rel_s4 @ X1 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl106]) ).
thf(zip_derived_cl8_001,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl143,plain,
! [X0: mu,X1: $i] :
( ~ ( exists_in_world @ X0 @ '#sk4' )
| ( defused @ X0 @ '#sk4' )
| ~ ( bomb @ X0 @ '#sk4' )
| ~ ( exists_in_world @ X0 @ '#sk4' )
| ~ ( rel_s4 @ X1 @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl138,zip_derived_cl8]) ).
thf(zip_derived_cl144,plain,
! [X0: mu,X1: $i] :
( ~ ( rel_s4 @ X1 @ '#sk4' )
| ~ ( bomb @ X0 @ '#sk4' )
| ( defused @ X0 @ '#sk4' )
| ~ ( exists_in_world @ X0 @ '#sk4' ) ),
inference(simplify,[status(thm)],[zip_derived_cl143]) ).
thf(zip_derived_cl156,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk4' )
| ( defused @ X0 @ '#sk4' )
| ~ ( bomb @ X0 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl144]) ).
thf(zip_derived_cl50,plain,
! [X2: mu] :
( ~ ( defused @ '#sk5' @ '#sk4' )
| ~ ( exists_in_world @ X2 @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl160,plain,
! [X0: mu] :
( ~ ( bomb @ '#sk5' @ '#sk4' )
| ~ ( exists_in_world @ '#sk5' @ '#sk4' )
| ~ ( exists_in_world @ X0 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl156,zip_derived_cl50]) ).
thf(ax2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( mand @ ( bomb @ X ) @ ( h @ A ) ) @ ( mbox_s4 @ ( bomb @ X ) ) ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i] :
~ ! [X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ~ ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ! [X10: mu] :
( ( exists_in_world @ X10 @ X8 )
=> ( ! [X12: $i] :
( ~ ( rel_s4 @ X8 @ X12 )
| ( bomb @ X10 @ X12 ) )
| ~ ( bomb @ X10 @ X8 )
| ~ ( h @ X6 @ X8 ) ) ) ) ) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( bomb @ Y3 @ Y4 ) ) )
| ( (~) @ ( bomb @ Y3 @ Y2 ) )
| ( (~) @ ( h @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( bomb @ Y2 @ Y3 ) ) )
| ( (~) @ ( bomb @ Y2 @ Y1 ) )
| ( (~) @ ( h @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
~ ( ( exists_in_world @ ( '#sk6' @ X2 ) @ X2 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( bomb @ Y1 @ Y2 ) ) )
| ( (~) @ ( bomb @ Y1 @ Y0 ) )
| ( (~) @ ( h @ ( '#sk6' @ X2 ) @ Y0 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk6' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl51,plain,
! [X2: mu] :
( ( bomb @ '#sk5' @ '#sk4' )
| ~ ( exists_in_world @ X2 @ '#sk4' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl72,plain,
bomb @ '#sk5' @ '#sk4',
inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl51]) ).
thf(zip_derived_cl46,plain,
exists_in_world @ '#sk5' @ '#sk4',
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl162,plain,
! [X0: mu] :
~ ( exists_in_world @ X0 @ '#sk4' ),
inference(demod,[status(thm)],[zip_derived_cl160,zip_derived_cl72,zip_derived_cl46]) ).
thf(zip_derived_cl63_002,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk6' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl43_003,plain,
rel_s4 @ '#sk3' @ '#sk4',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(cumulative_ax,axiom,
! [X: mu,V: $i,W: $i] :
( ( ( rel_s4 @ V @ W )
& ( exists_in_world @ X @ V ) )
=> ( exists_in_world @ X @ W ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( exists_in_world @ Y0 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[cumulative_ax]) ).
thf(zip_derived_cl11,plain,
! [X2: mu] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( exists_in_world @ X2 @ Y0 ) )
=> ( exists_in_world @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl12,plain,
! [X2: mu,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X4 @ Y0 )
& ( exists_in_world @ X2 @ X4 ) )
=> ( exists_in_world @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl13,plain,
! [X2: mu,X4: $i,X6: $i] :
( ( ( rel_s4 @ X4 @ X6 )
& ( exists_in_world @ X2 @ X4 ) )
=> ( exists_in_world @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl14,plain,
! [X2: mu,X4: $i,X6: $i] :
( ~ ( ( rel_s4 @ X4 @ X6 )
& ( exists_in_world @ X2 @ X4 ) )
| ( exists_in_world @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: mu,X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( exists_in_world @ X2 @ X4 )
| ( exists_in_world @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl56,plain,
! [X0: mu] :
( ( exists_in_world @ X0 @ '#sk4' )
| ~ ( exists_in_world @ X0 @ '#sk3' ) ),
inference('sup-',[status(thm)],[zip_derived_cl43,zip_derived_cl15]) ).
thf(zip_derived_cl96,plain,
exists_in_world @ ( '#sk6' @ '#sk3' ) @ '#sk4',
inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl56]) ).
thf(zip_derived_cl166,plain,
$false,
inference('sup+',[status(thm)],[zip_derived_cl162,zip_derived_cl96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : PLA032^7 : TPTP v8.1.2. Released v5.5.0.
% 0.12/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.lzY2jXvp4F true
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Aug 27 05:59:27 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % Running portfolio for 300 s
% 0.15/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.22/0.63 % Total configuration time : 828
% 0.22/0.63 % Estimated wc time : 1656
% 0.22/0.63 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /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
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.47/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.47/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.55/0.84 % Solved by lams/35_full_unif4.sh.
% 1.55/0.84 % done 61 iterations in 0.070s
% 1.55/0.84 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.55/0.84 % SZS output start Refutation
% See solution above
% 1.55/0.84
% 1.55/0.84
% 1.55/0.84 % Terminating...
% 1.84/0.95 % Runner terminated.
% 1.84/0.96 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------