TSTP Solution File: PHI003^1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI003^1 : TPTP v8.1.2. Released v6.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dcZx9T6i1o true
% Computer : n011.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 12:58:47 EDT 2023
% Result : Theorem 97.48s 13.40s
% Output : Refutation 97.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 54
% Syntax : Number of formulae : 106 ( 42 unt; 20 typ; 0 def)
% Number of atoms : 311 ( 40 equ; 19 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 787 ( 52 ~; 33 |; 18 &; 564 @)
% ( 8 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 19 usr; 6 con; 0-4 aty)
% ( 54 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 264 ( 174 ^; 80 !; 10 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(mdia_type,type,
mdia: ( $i > $o ) > $i > $o ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf('#sk2_type',type,
'#sk2': $i > mu > mu > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(positive_type,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf('#sk20274_type',type,
'#sk20274': $i > ( mu > $i > $o ) > mu ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(mbox_generic_type,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mdia_generic_type,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mequiv_type,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(mforall_indset_type,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf(god_type,type,
god: mu > $i > $o ).
thf(mbox_type,type,
mbox: ( $i > $o ) > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk20249_type',type,
'#sk20249': $i > ( mu > $i > $o ) > $i ).
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(mbox,axiom,
( mbox
= ( mbox_generic @ rel ) ) ).
thf(mbox_generic,axiom,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ) ).
thf('2',plain,
( mbox_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_generic]) ).
thf('3',plain,
( mbox_generic
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
! [X4: $i] :
( ( V_2 @ X4 )
| ~ ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('4',plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mbox,'3']) ).
thf('5',plain,
( mbox
= ( mbox_generic @ rel ) ),
define([status(thm)]) ).
thf(mforall_indset,axiom,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
thf('6',plain,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_indset]) ).
thf('7',plain,
( mforall_indset
= ( ^ [V_1: ( mu > $i > $o ) > $i > $o,V_2: $i] :
! [X4: mu > $i > $o] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ) ).
thf('8',plain,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).
thf('9',plain,
( mforall_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ) ).
thf('10',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies]) ).
thf('11',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
=> ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
& ( Psi @ W ) ) ) ) ).
thf('12',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
& ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand]) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o,V_3: $i] :
( ( V_1 @ V_3 )
& ( V_2 @ V_3 ) ) ) ),
define([status(thm)]) ).
thf(axA2,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mforall_indset
@ ^ [Psi: mu > $i > $o] :
( mimplies
@ ( mand @ ( positive @ Phi )
@ ( mbox
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( Phi @ X ) @ ( Psi @ X ) ) ) ) )
@ ( positive @ Psi ) ) ) ) ) ).
thf(zf_stmt_0,axiom,
! [X4: $i,X6: mu > $i > $o,X8: mu > $i > $o] :
( ( ! [X10: $i] :
( ~ ( rel @ X4 @ X10 )
| ! [X12: mu] :
( ( X6 @ X12 @ X10 )
=> ( X8 @ X12 @ X10 ) ) )
& ( positive @ X6 @ X4 ) )
=> ( positive @ X8 @ X4 ) ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu > $i > $o] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel @ Y0 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( Y1 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
& ( positive @ Y1 @ Y0 ) )
=> ( positive @ Y2 @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel @ X2 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
& ( positive @ Y0 @ X2 ) )
=> ( positive @ Y1 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl66,plain,
! [X2: $i,X4: mu > $i > $o] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( X4 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive @ X4 @ X2 ) )
=> ( positive @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl68,plain,
! [X0: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ X0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
& ( positive
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ X0 ) )
=> ( positive @ Y0 @ X0 ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl890,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
& ( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 ) )
=> ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(defD1,axiom,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ) ).
thf('14',plain,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[defD1,'7','11']) ).
thf('15',plain,
( god
= ( ^ [V_1: mu] :
( mforall_indset
@ ^ [V_2: mu > $i > $o] : ( mimplies @ ( positive @ V_2 ) @ ( V_2 @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(axA3,axiom,
mvalid @ ( positive @ god ) ).
thf(zf_stmt_1,axiom,
! [X4: $i] :
( positive
@ ^ [V_1: mu,V_2: $i] :
! [X6: mu > $i > $o] :
( ( positive @ X6 @ V_2 )
=> ( X6 @ V_1 @ V_2 ) )
@ X4 ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( positive
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl13,plain,
! [X2: $i] :
( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl895,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
& $true )
=> ( positive @ X2 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl890,zip_derived_cl13]) ).
thf(zip_derived_cl896,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
=> ( positive @ X2 @ X0 ) ),
inference('simplify boolean subterms',[status(thm)],[zip_derived_cl895]) ).
thf(zip_derived_cl897,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ X0 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( X2 @ Y1 @ Y0 ) ) ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl896]) ).
thf(zip_derived_cl898,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( ( (~) @ ( rel @ X0 @ ( '#sk20249' @ X0 @ X2 ) ) )
| ( !!
@ ^ [Y0: mu] :
( ( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk20249' @ X0 @ X2 ) )
=> ( Y1 @ Y0 @ ( '#sk20249' @ X0 @ X2 ) ) ) )
=> ( X2 @ Y0 @ ( '#sk20249' @ X0 @ X2 ) ) ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl897]) ).
thf(zip_derived_cl899,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( rel @ X0 @ ( '#sk20249' @ X0 @ X2 ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl898]) ).
thf(mdia,axiom,
( mdia
= ( mdia_generic @ rel ) ) ).
thf(mdia_generic,axiom,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ) ).
thf('16',plain,
( mdia_generic
= ( ^ [R: $i > $i > $o,Phi: $i > $o,W: $i] :
? [V: $i] :
( ( Phi @ V )
& ( R @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mdia_generic]) ).
thf('17',plain,
( mdia_generic
= ( ^ [V_1: $i > $i > $o,V_2: $i > $o,V_3: $i] :
? [X4: $i] :
( ( V_2 @ X4 )
& ( V_1 @ V_3 @ X4 ) ) ) ),
define([status(thm)]) ).
thf('18',plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mdia,'17']) ).
thf('19',plain,
( mdia
= ( mdia_generic @ rel ) ),
define([status(thm)]) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ) ).
thf('20',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind]) ).
thf('21',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
? [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(corC,conjecture,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) ).
thf(zf_stmt_2,conjecture,
! [X4: $i] :
? [X6: $i] :
( ( rel @ X4 @ X6 )
& ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ) ).
thf(zf_stmt_3,negated_conjecture,
~ ! [X4: $i] :
? [X6: $i] :
( ( rel @ X4 @ X6 )
& ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl5,plain,
~ ( !!
@ ^ [Y0: $i] :
( ??
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
& ( ??
@ ^ [Y2: mu] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl6,plain,
~ ( ??
@ ^ [Y0: $i] :
( ( rel @ '#sk1' @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i] :
~ ( ( rel @ '#sk1' @ X2 )
& ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X2 )
=> ( Y1 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl8,plain,
! [X2: $i] :
( ~ ( rel @ '#sk1' @ X2 )
| ~ ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X2 )
=> ( Y1 @ Y0 @ X2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl9,plain,
! [X2: $i,X4: mu] :
( ~ ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X2 )
=> ( Y0 @ X4 @ X2 ) ) )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl10,plain,
! [X2: $i,X4: mu] :
( ~ ( ( positive @ ( '#sk2' @ X2 @ X4 ) @ X2 )
=> ( '#sk2' @ X2 @ X4 @ X4 @ X2 ) )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl11,plain,
! [X2: $i,X4: mu] :
( ( positive @ ( '#sk2' @ X2 @ X4 ) @ X2 )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl900,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( !!
@ ^ [Y0: mu] :
( ( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk20249' @ X0 @ X2 ) )
=> ( Y1 @ Y0 @ ( '#sk20249' @ X0 @ X2 ) ) ) )
=> ( X2 @ Y0 @ ( '#sk20249' @ X0 @ X2 ) ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl898]) ).
thf(zip_derived_cl901,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( '#sk20249' @ X0 @ X2 ) )
=> ( Y0 @ ( '#sk20274' @ X0 @ X2 ) @ ( '#sk20249' @ X0 @ X2 ) ) ) )
=> ( X2 @ ( '#sk20274' @ X0 @ X2 ) @ ( '#sk20249' @ X0 @ X2 ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl900]) ).
thf(zip_derived_cl902,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( '#sk20249' @ X0 @ X2 ) )
=> ( Y0 @ ( '#sk20274' @ X0 @ X2 ) @ ( '#sk20249' @ X0 @ X2 ) ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl901]) ).
thf(zip_derived_cl904,plain,
! [X0: $i,X2: mu > $i > $o,X4: mu > $i > $o] :
( ( ( positive @ X4 @ ( '#sk20249' @ X0 @ X2 ) )
=> ( X4 @ ( '#sk20274' @ X0 @ X2 ) @ ( '#sk20249' @ X0 @ X2 ) ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl902]) ).
thf(zip_derived_cl909,plain,
! [X0: $i,X2: mu > $i > $o,X4: mu > $i > $o] :
( ~ ( positive @ X4 @ ( '#sk20249' @ X0 @ X2 ) )
| ( X4 @ ( '#sk20274' @ X0 @ X2 ) @ ( '#sk20249' @ X0 @ X2 ) )
| ( positive @ X2 @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl904]) ).
thf(zip_derived_cl1229,plain,
! [X0: mu > $i > $o,X1: $i,X2: mu] :
( ~ ( rel @ '#sk1' @ ( '#sk20249' @ X1 @ X0 ) )
| ( positive @ X0 @ X1 )
| ( '#sk2' @ ( '#sk20249' @ X1 @ X0 ) @ X2 @ ( '#sk20274' @ X1 @ X0 ) @ ( '#sk20249' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl11,zip_derived_cl909]) ).
thf(zip_derived_cl12,plain,
! [X2: $i,X4: mu] :
( ~ ( '#sk2' @ X2 @ X4 @ X4 @ X2 )
| ~ ( rel @ '#sk1' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl1361,plain,
! [X0: mu > $i > $o,X1: $i] :
( ( positive @ X0 @ X1 )
| ~ ( rel @ '#sk1' @ ( '#sk20249' @ X1 @ X0 ) )
| ~ ( rel @ '#sk1' @ ( '#sk20249' @ X1 @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1229,zip_derived_cl12]) ).
thf(zip_derived_cl1362,plain,
! [X0: mu > $i > $o,X1: $i] :
( ~ ( rel @ '#sk1' @ ( '#sk20249' @ X1 @ X0 ) )
| ( positive @ X0 @ X1 ) ),
inference(simplify,[status(thm)],[zip_derived_cl1361]) ).
thf(zip_derived_cl1365,plain,
! [X0: mu > $i > $o] :
( ( positive @ X0 @ '#sk1' )
| ( positive @ X0 @ '#sk1' ) ),
inference('sup-',[status(thm)],[zip_derived_cl899,zip_derived_cl1362]) ).
thf(zip_derived_cl1376,plain,
! [X0: mu > $i > $o] : ( positive @ X0 @ '#sk1' ),
inference(simplify,[status(thm)],[zip_derived_cl1365]) ).
thf(mequiv,axiom,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ) ).
thf('22',plain,
( mequiv
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
<=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mequiv]) ).
thf('23',plain,
( mequiv
= ( ^ [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('24',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('25',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf(axA1,axiom,
( mvalid
@ ( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mequiv
@ ( positive
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) )
@ ( mnot @ ( positive @ Phi ) ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: mu > $i > $o] :
( ( positive
@ ^ [V_1: mu,V_2: $i] :
~ ( X6 @ V_1 @ V_2 )
@ X4 )
<=> ~ ( positive @ X6 @ X4 ) ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive
@ ^ [Y2: mu,Y3: $i] : ( (~) @ ( Y1 @ Y2 @ Y3 ) )
@ Y0 )
<=> ( (~) @ ( positive @ Y1 @ Y0 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl18,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive
@ ^ [Y1: mu,Y2: $i] : ( (~) @ ( Y0 @ Y1 @ Y2 ) )
@ X2 )
<=> ( (~) @ ( positive @ Y0 @ X2 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl19,plain,
! [X2: $i,X4: mu > $i > $o] :
( ( positive
@ ^ [Y0: mu,Y1: $i] : ( (~) @ ( X4 @ Y0 @ Y1 ) )
@ X2 )
<=> ( (~) @ ( positive @ X4 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl20,plain,
! [X0: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
( (~)
@ ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
@ X0 )
<=> ( (~)
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 ) ) ),
inference(triggered_bool_instantiation,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl129,plain,
! [X0: $i] :
( ( positive
@ ^ [Y0: mu,Y1: $i] :
( (~)
@ ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
@ X0 )
!= ( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 ) ),
inference('simplify nested equalities',[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl13_001,plain,
! [X2: $i] :
( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl130,plain,
! [X0: $i] :
~ ( positive
@ ^ [Y0: mu,Y1: $i] :
( (~)
@ ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
@ X0 ),
inference(demod,[status(thm)],[zip_derived_cl129,zip_derived_cl13]) ).
thf(zip_derived_cl1383,plain,
$false,
inference('sup-',[status(thm)],[zip_derived_cl1376,zip_derived_cl130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : PHI003^1 : TPTP v8.1.2. Released v6.1.0.
% 0.05/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.dcZx9T6i1o true
% 0.10/0.31 % Computer : n011.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Aug 27 08:59:39 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.32 % Number of cores: 8
% 0.10/0.32 % Python version: Python 3.6.8
% 0.10/0.32 % Running in HO mode
% 0.15/0.52 % Total configuration time : 828
% 0.15/0.52 % Estimated wc time : 1656
% 0.15/0.52 % Estimated cpu time (8 cpus) : 207.0
% 0.15/0.60 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.15/0.61 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.15/0.61 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.15/0.61 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.15/0.62 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.15/0.62 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.15/0.62 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.15/0.65 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.05/0.69 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.05/0.70 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 97.48/13.40 % Solved by lams/35_full_unif4.sh.
% 97.48/13.40 % done 197 iterations in 12.736s
% 97.48/13.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 97.48/13.40 % SZS output start Refutation
% See solution above
% 97.48/13.40
% 97.48/13.40
% 97.48/13.41 % Terminating...
% 98.56/13.61 % Runner terminated.
% 98.56/13.63 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------