TSTP Solution File: PHI005^2 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : PHI005^2 : TPTP v8.1.2. Released v6.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EGtArhmBNu true
% Computer : n028.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 12:58:49 EDT 2023
% Result : Theorem 1.74s 1.02s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 57
% Syntax : Number of formulae : 128 ( 46 unt; 23 typ; 0 def)
% Number of atoms : 364 ( 36 equ; 10 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1023 ( 51 ~; 49 |; 7 &; 771 @)
% ( 0 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 269 ( 269 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 22 usr; 6 con; 0-4 aty)
% ( 59 !!; 18 ??; 0 @@+; 0 @@-)
% Number of variables : 321 ( 200 ^; 110 !; 11 ?; 321 :)
% 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('#sk5_type',type,
'#sk5': $i > mu ).
thf(rel_type,type,
rel: $i > $i > $o ).
thf(necessary_existence_type,type,
necessary_existence: mu > $i > $o ).
thf(msymmetric_type,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf('#sk10_type',type,
'#sk10': $i > mu > mu > $i > $o ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk35_type',type,
'#sk35': ( mu > $i > $o ) > $i > mu ).
thf('#sk2_type',type,
'#sk2': $i ).
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(positive_type,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(mdia_generic_type,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(essence_type,type,
essence: ( mu > $i > $o ) > mu > $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('#sk3_type',type,
'#sk3': mu > mu > $i > $o ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i > $i ).
thf(defD1,axiom,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ) ).
thf(mforall_indset,axiom,
( mforall_indset
= ( ^ [Phi: ( mu > $i > $o ) > $i > $o,W: $i] :
! [X: mu > $i > $o] : ( Phi @ X @ W ) ) ) ).
thf('0',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('1',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(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ) ).
thf('2',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
=> ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies]) ).
thf('3',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('4',plain,
( god
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] : ( mimplies @ ( positive @ Phi ) @ ( Phi @ X ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[defD1,'1','3']) ).
thf('5',plain,
( god
= ( ^ [V_1: mu] :
( mforall_indset
@ ^ [V_2: mu > $i > $o] : ( mimplies @ ( positive @ V_2 ) @ ( V_2 @ V_1 ) ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('6',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('7',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('8',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('9',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('10',plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mbox,'9']) ).
thf('11',plain,
( mbox
= ( mbox_generic @ rel ) ),
define([status(thm)]) ).
thf(mexists_ind,axiom,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ) ).
thf('12',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
? [X: mu] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind]) ).
thf('13',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
? [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(thmT3,conjecture,
( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel @ X4 @ X6 )
| ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ) ).
thf(zf_stmt_1,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_0]) ).
thf(zip_derived_cl4,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_1]) ).
thf(zip_derived_cl10,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_cl4]) ).
thf(zip_derived_cl11,plain,
~ ( ( (~) @ ( rel @ '#sk1' @ '#sk2' ) )
| ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ '#sk2' )
=> ( Y1 @ Y0 @ '#sk2' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl13,plain,
~ ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ '#sk2' )
=> ( Y1 @ Y0 @ '#sk2' ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl14,plain,
! [X2: mu] :
~ ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ '#sk2' )
=> ( Y0 @ X2 @ '#sk2' ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl15,plain,
! [X2: mu] :
~ ( ( positive @ ( '#sk3' @ X2 ) @ '#sk2' )
=> ( '#sk3' @ X2 @ X2 @ '#sk2' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl16,plain,
! [X2: mu] : ( positive @ ( '#sk3' @ X2 ) @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl16_001,plain,
! [X2: mu] : ( positive @ ( '#sk3' @ X2 ) @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
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('14',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('15',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('16',plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(simplify_rw_rule,[status(thm)],[mdia,'15']) ).
thf('17',plain,
( mdia
= ( mdia_generic @ rel ) ),
define([status(thm)]) ).
thf(corC,axiom,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X: mu] : ( god @ X ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
? [X6: $i] :
( ( rel @ X4 @ X6 )
& ? [X8: mu] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ X6 )
=> ( X10 @ X8 @ X6 ) ) ) ).
thf(zip_derived_cl2,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_2]) ).
thf(zip_derived_cl22,plain,
! [X2: $i] :
( ??
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
& ( ??
@ ^ [Y1: mu] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl23,plain,
! [X2: $i] :
( ( rel @ X2 @ ( '#sk4' @ X2 ) )
& ( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk4' @ X2 ) )
=> ( Y1 @ Y0 @ ( '#sk4' @ X2 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl24,plain,
! [X2: $i] : ( rel @ X2 @ ( '#sk4' @ X2 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(msymmetric,axiom,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ) ).
thf('18',plain,
( msymmetric
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i] :
( ( R @ S @ T )
=> ( R @ T @ S ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[msymmetric]) ).
thf('19',plain,
( msymmetric
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i] :
( ( V_1 @ X4 @ X6 )
=> ( V_1 @ X6 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(sym,axiom,
msymmetric @ rel ).
thf(zf_stmt_3,axiom,
! [X4: $i,X6: $i] :
( ( rel @ X4 @ X6 )
=> ( rel @ X6 @ X4 ) ) ).
thf(zip_derived_cl0,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
=> ( rel @ Y1 @ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl5,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( rel @ X2 @ Y0 )
=> ( rel @ Y0 @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl6,plain,
! [X2: $i,X4: $i] :
( ( rel @ X2 @ X4 )
=> ( rel @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl7,plain,
! [X2: $i,X4: $i] :
( ~ ( rel @ X2 @ X4 )
| ( rel @ X4 @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl30,plain,
! [X0: $i] : ( rel @ ( '#sk4' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl7]) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ) ).
thf('20',plain,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] : ( Phi @ X @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).
thf('21',plain,
( mforall_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] : ( V_1 @ X4 @ V_2 ) ) ),
define([status(thm)]) ).
thf(thmT2,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X: mu] : ( mimplies @ ( god @ X ) @ ( essence @ god @ X ) ) ) ) ).
thf(zf_stmt_4,axiom,
! [X4: $i,X6: mu] :
( ! [X8: mu > $i > $o] :
( ( positive @ X8 @ X4 )
=> ( X8 @ X6 @ X4 ) )
=> ( essence
@ ^ [V_1: mu,V_2: $i] :
! [X10: mu > $i > $o] :
( ( positive @ X10 @ V_2 )
=> ( X10 @ V_1 @ V_2 ) )
@ X6
@ X4 ) ) ).
thf(zip_derived_cl3,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: mu] :
( ( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( essence
@ ^ [Y2: mu,Y3: $i] :
( !!
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl34,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu] :
( ( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X2 )
=> ( Y1 @ Y0 @ X2 ) ) )
=> ( essence
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ Y0
@ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: mu] :
( ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X2 )
=> ( Y0 @ X4 @ X2 ) ) )
=> ( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X4
@ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: mu] :
( ~ ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X2 )
=> ( Y0 @ X4 @ X2 ) ) )
| ( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X4
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: mu] :
( ~ ( ( positive @ ( '#sk10' @ X2 @ X4 ) @ X2 )
=> ( '#sk10' @ X2 @ X4 @ X4 @ X2 ) )
| ( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X4
@ X2 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: mu] :
( ( positive @ ( '#sk10' @ X2 @ X4 ) @ X2 )
| ( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X4
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(defD3,axiom,
( necessary_existence
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( essence @ Phi @ X )
@ ( mbox
@ ( mexists_ind
@ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ) ).
thf('22',plain,
( necessary_existence
= ( ^ [X: mu] :
( mforall_indset
@ ^ [Phi: mu > $i > $o] :
( mimplies @ ( essence @ Phi @ X )
@ ( mbox
@ ( mexists_ind
@ ^ [Y: mu] : ( Phi @ Y ) ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[defD3,'11','9','13','1','3']) ).
thf('23',plain,
( necessary_existence
= ( ^ [V_1: mu] :
( mforall_indset
@ ^ [V_2: mu > $i > $o] :
( mimplies @ ( essence @ V_2 @ V_1 )
@ ( mbox
@ ( mexists_ind
@ ^ [V_3: mu] : ( V_2 @ V_3 ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(axA5,axiom,
mvalid @ ( positive @ necessary_existence ) ).
thf(zf_stmt_5,axiom,
! [X4: $i] :
( positive
@ ^ [V_1: mu,V_2: $i] :
! [X6: mu > $i > $o] :
( ( essence @ X6 @ V_1 @ V_2 )
=> ! [X8: $i] :
( ~ ( rel @ V_2 @ X8 )
| ? [X10: mu] : ( X6 @ X10 @ X8 ) ) )
@ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] :
( positive
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( essence @ Y3 @ Y1 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel @ Y2 @ Y4 ) )
| ( ??
@ ^ [Y5: mu] : ( Y3 @ Y5 @ Y4 ) ) ) ) ) )
@ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl32,plain,
! [X2: $i] :
( positive
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel @ Y1 @ Y3 ) )
| ( ??
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
( ??
@ ^ [Y0: mu] :
( !!
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( '#sk4' @ X2 ) )
=> ( Y1 @ Y0 @ ( '#sk4' @ X2 ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( '#sk4' @ X2 ) )
=> ( Y0 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl27,plain,
! [X2: $i,X4: mu > $i > $o] :
( ( positive @ X4 @ ( '#sk4' @ X2 ) )
=> ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: mu > $i > $o] :
( ~ ( positive @ X4 @ ( '#sk4' @ X2 ) )
| ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl58,plain,
! [X0: $i] :
( ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel @ Y1 @ Y3 ) )
| ( ??
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ ( '#sk5' @ X0 )
@ ( '#sk4' @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl29]) ).
thf(zip_derived_cl68,plain,
! [X0: $i] :
( !!
@ ^ [Y0: mu > $i > $o] :
( ( essence @ Y0 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y1 ) )
| ( ??
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y0 ) )
| ( ??
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl81,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ Y0 ) )
| ( ??
@ ^ [Y1: mu] : ( X2 @ Y1 @ Y0 ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl82,plain,
! [X0: $i,X2: mu > $i > $o,X4: $i] :
( ( (~) @ ( rel @ ( '#sk4' @ X0 ) @ X4 ) )
| ( ??
@ ^ [Y0: mu] : ( X2 @ Y0 @ X4 ) )
| ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl83,plain,
! [X0: $i,X2: mu > $i > $o,X4: $i] :
( ~ ( rel @ ( '#sk4' @ X0 ) @ X4 )
| ( ??
@ ^ [Y0: mu] : ( X2 @ Y0 @ X4 ) )
| ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X0: $i,X2: mu > $i > $o,X4: $i] :
( ( X2 @ ( '#sk35' @ X2 @ X4 ) @ X4 )
| ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl85,plain,
! [X0: $i,X1: $i] :
( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
| ( ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl39,zip_derived_cl84]) ).
thf(zip_derived_cl93,plain,
! [X0: $i,X1: $i] :
( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
| ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0
@ ( '#sk35'
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ X1 )
@ X1 ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl109,plain,
! [X0: $i,X1: $i,X3: mu > $i > $o] :
( ( ( positive @ X3 @ X1 )
=> ( X3
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X1 )
| ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl114,plain,
! [X0: $i,X1: $i,X3: mu > $i > $o] :
( ~ ( positive @ X3 @ X1 )
| ( X3
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 )
| ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X1 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl109]) ).
thf(zip_derived_cl115,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( positive @ ( '#sk10' @ ( '#sk4' @ X0 ) @ ( '#sk5' @ X0 ) ) @ ( '#sk4' @ X0 ) )
| ( X1
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 )
@ X0 )
| ~ ( positive @ X1 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl30,zip_derived_cl114]) ).
thf(zip_derived_cl123,plain,
! [X0: mu] :
( ( '#sk3' @ X0
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ '#sk2' )
@ '#sk2' )
| ( positive @ ( '#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) ) @ ( '#sk4' @ '#sk2' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl115]) ).
thf(zip_derived_cl17,plain,
! [X2: mu] :
~ ( '#sk3' @ X2 @ X2 @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl127,plain,
positive @ ( '#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) ) @ ( '#sk4' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl123,zip_derived_cl17]) ).
thf(zip_derived_cl29_002,plain,
! [X2: $i,X4: mu > $i > $o] :
( ~ ( positive @ X4 @ ( '#sk4' @ X2 ) )
| ( X4 @ ( '#sk5' @ X2 ) @ ( '#sk4' @ X2 ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl129,plain,
'#sk10' @ ( '#sk4' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) @ ( '#sk5' @ '#sk2' ) @ ( '#sk4' @ '#sk2' ),
inference('sup-',[status(thm)],[zip_derived_cl127,zip_derived_cl29]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: mu] :
( ~ ( '#sk10' @ X2 @ X4 @ X4 @ X2 )
| ( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X4
@ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl133,plain,
( essence
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( '#sk5' @ '#sk2' )
@ ( '#sk4' @ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl40]) ).
thf(zip_derived_cl84_003,plain,
! [X0: $i,X2: mu > $i > $o,X4: $i] :
( ( X2 @ ( '#sk35' @ X2 @ X4 ) @ X4 )
| ~ ( essence @ X2 @ ( '#sk5' @ X0 ) @ ( '#sk4' @ X0 ) )
| ~ ( rel @ ( '#sk4' @ X0 ) @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl135,plain,
! [X0: $i] :
( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 )
| ( ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 )
@ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl133,zip_derived_cl84]) ).
thf(zip_derived_cl136,plain,
! [X0: $i] :
( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 )
| ( !!
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X0 )
=> ( Y0
@ ( '#sk35'
@ ^ [Y1: mu,Y2: $i] :
( !!
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ X0 )
@ X0 ) ) ) ),
inference(ho_norm,[status(thm)],[zip_derived_cl135]) ).
thf(zip_derived_cl162,plain,
! [X0: $i,X2: mu > $i > $o] :
( ( ( positive @ X2 @ X0 )
=> ( X2
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 )
@ X0 ) )
| ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl136]) ).
thf(zip_derived_cl167,plain,
! [X0: $i,X2: mu > $i > $o] :
( ~ ( positive @ X2 @ X0 )
| ( X2
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X0 )
@ X0 )
| ~ ( rel @ ( '#sk4' @ '#sk2' ) @ X0 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl162]) ).
thf(zip_derived_cl171,plain,
! [X0: mu] :
( ~ ( rel @ ( '#sk4' @ '#sk2' ) @ '#sk2' )
| ( '#sk3' @ X0
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ '#sk2' )
@ '#sk2' ) ),
inference('sup-',[status(thm)],[zip_derived_cl16,zip_derived_cl167]) ).
thf(zip_derived_cl30_004,plain,
! [X0: $i] : ( rel @ ( '#sk4' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl24,zip_derived_cl7]) ).
thf(zip_derived_cl176,plain,
! [X0: mu] :
( '#sk3' @ X0
@ ( '#sk35'
@ ^ [Y0: mu,Y1: $i] :
( !!
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ '#sk2' )
@ '#sk2' ),
inference(demod,[status(thm)],[zip_derived_cl171,zip_derived_cl30]) ).
thf(zip_derived_cl17_005,plain,
! [X2: mu] :
~ ( '#sk3' @ X2 @ X2 @ '#sk2' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl178,plain,
$false,
inference('sup-',[status(thm)],[zip_derived_cl176,zip_derived_cl17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : PHI005^2 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EGtArhmBNu true
% 0.14/0.35 % Computer : n028.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 : Sun Aug 27 09:14:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % 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
% 0.22/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.22/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.22/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 0.22/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 1.49/0.92 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
% 1.74/1.02 % Solved by lams/35_full_unif4.sh.
% 1.74/1.02 % done 44 iterations in 0.216s
% 1.74/1.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 1.74/1.02 % SZS output start Refutation
% See solution above
% 1.74/1.02
% 1.74/1.02
% 1.74/1.02 % Terminating...
% 1.75/1.14 % Runner terminated.
% 1.89/1.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------