TSTP Solution File: KRS272^7 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : KRS272^7 : 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.6pP51py24J true
% Computer : n001.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 05:57:03 EDT 2023
% Result : Theorem 41.70s 5.96s
% Output : Refutation 41.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 64
% Number of leaves : 62
% Syntax : Number of formulae : 288 ( 65 unt; 29 typ; 0 def)
% Number of atoms : 2103 ( 30 equ; 341 cnn)
% Maximal formula atoms : 33 ( 8 avg)
% Number of connectives : 8251 (1256 ~;1085 |; 15 &;5584 @)
% ( 0 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 13 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 28 usr; 7 con; 0-4 aty)
% ( 173 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 825 ( 239 ^; 586 !; 0 ?; 825 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf(string_type,type,
string: mu > $i > $o ).
thf(number_type,type,
number: mu > mu > $i > $o ).
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(userid_type,type,
userid: mu > mu > $i > $o ).
thf('#sk8_type',type,
'#sk8': mu > mu > mu > mu > mu ).
thf('#sk3_type',type,
'#sk3': $i > mu ).
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': mu > mu > $i ).
thf(mexists_ind_type,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(one_type,type,
one: mu ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(do_type,type,
do: mu > mu > mu > $i > $o ).
thf('#sk9_type',type,
'#sk9': $i > mu > mu > mu > mu ).
thf(u_type,type,
u: mu ).
thf(mtransitive_type,type,
mtransitive: ( $i > $i > $o ) > $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('#sk6_type',type,
'#sk6': mu > mu > mu > mu > $i ).
thf(entry_box_type,type,
entry_box: mu > $i > $o ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf(in_type,type,
in: mu > mu > mu > $i > $o ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#sk2_type',type,
'#sk2': $i > mu ).
thf('#sk5_type',type,
'#sk5': $i ).
thf(mreflexive,axiom,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ) ).
thf('0',plain,
( mreflexive
= ( ^ [R: $i > $i > $o] :
! [S: $i] : ( R @ S @ S ) ) ),
inference(simplify_rw_rule,[status(thm)],[mreflexive]) ).
thf('1',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_0,axiom,
! [X4: $i] : ( rel_s4 @ X4 @ X4 ) ).
thf(zip_derived_cl1,plain,
( !!
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl10,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('2',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('3',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('4',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('5',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('6',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('7',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('8',plain,
( mnot
= ( ^ [Phi: $i > $o,W: $i] :
~ ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mnot]) ).
thf('9',plain,
( mnot
= ( ^ [V_1: $i > $o,V_2: $i] :
~ ( V_1 @ V_2 ) ) ),
define([status(thm)]) ).
thf('10',plain,
( mexists_ind
= ( ^ [Phi: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X: mu] : ( mnot @ ( Phi @ X ) ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mexists_ind,'7','9']) ).
thf('11',plain,
( mexists_ind
= ( ^ [V_1: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [V_2: mu] : ( 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(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('12',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('13',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('14',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'13','9']) ).
thf('15',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(ax1,axiom,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [I: mu] : ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( string @ I ) ) ) ) ) ) ).
thf(zf_stmt_1,axiom,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ~ ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ~ ( string @ X8 @ X10 )
| ~ ( userid @ u @ X8 @ X10 ) ) ) ) ) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~) @ ( string @ Y2 @ Y3 ) )
| ( (~) @ ( userid @ u @ Y2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl33,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~) @ ( string @ Y1 @ Y2 ) )
| ( (~) @ ( userid @ u @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl34,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X4 ) )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( (~)
@ ( ( (~) @ ( string @ Y0 @ Y1 ) )
| ( (~) @ ( userid @ u @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl35,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( (~)
@ ( ( (~) @ ( string @ Y0 @ Y1 ) )
| ( (~) @ ( userid @ u @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl36,plain,
! [X2: $i,X4: $i] :
( ~ ( ( exists_in_world @ ( '#sk3' @ X4 ) @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( string @ ( '#sk3' @ X4 ) @ Y0 ) )
| ( (~) @ ( userid @ u @ ( '#sk3' @ X4 ) @ Y0 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl38,plain,
! [X2: $i,X4: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( string @ ( '#sk3' @ X4 ) @ Y0 ) )
| ( (~) @ ( userid @ u @ ( '#sk3' @ X4 ) @ Y0 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl39,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( (~) @ ( rel_s4 @ X4 @ X6 ) )
| ( (~)
@ ( ( (~) @ ( string @ ( '#sk3' @ X4 ) @ X6 ) )
| ( (~) @ ( userid @ u @ ( '#sk3' @ X4 ) @ X6 ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl40,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ( (~) @ ( string @ ( '#sk3' @ X4 ) @ X6 ) )
| ( (~) @ ( userid @ u @ ( '#sk3' @ X4 ) @ X6 ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl41,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( string @ ( '#sk3' @ X4 ) @ X6 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( rel_s4 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl129,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( string @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl41]) ).
thf(ax2,axiom,
( mvalid
@ ( mexists_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) ) ) ).
thf(zf_stmt_2,axiom,
! [X4: $i] :
~ ! [X6: mu] :
( ( exists_in_world @ X6 @ X4 )
=> ~ ! [X8: $i] :
( ~ ( rel_s4 @ X4 @ X8 )
| ~ ( ~ ( number @ X6 @ one @ X8 )
| ~ ( entry_box @ X6 @ X8 ) ) ) ) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: $i] :
( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~) @ ( number @ Y1 @ one @ Y2 ) )
| ( (~) @ ( entry_box @ Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_2]) ).
thf(zip_derived_cl25,plain,
! [X2: $i] :
~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( (~)
@ ( ( (~) @ ( number @ Y0 @ one @ Y1 ) )
| ( (~) @ ( entry_box @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl26,plain,
! [X2: $i] :
~ ( ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( number @ ( '#sk2' @ X2 ) @ one @ Y0 ) )
| ( (~) @ ( entry_box @ ( '#sk2' @ X2 ) @ Y0 ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl28,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( number @ ( '#sk2' @ X2 ) @ one @ Y0 ) )
| ( (~) @ ( entry_box @ ( '#sk2' @ X2 ) @ Y0 ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl29,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X4 ) )
| ( (~)
@ ( ( (~) @ ( number @ ( '#sk2' @ X2 ) @ one @ X4 ) )
| ( (~) @ ( entry_box @ ( '#sk2' @ X2 ) @ X4 ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl30,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( ( (~) @ ( number @ ( '#sk2' @ X2 ) @ one @ X4 ) )
| ( (~) @ ( entry_box @ ( '#sk2' @ X2 ) @ X4 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl32,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl32_001,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl10_002,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf('16',plain,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'13','9']) ).
thf('17',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(ax3,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S: mu] :
( mforall_ind
@ ^ [I: mu] :
( mforall_ind
@ ^ [B: mu] :
( mimplies @ ( mand @ ( string @ I ) @ ( entry_box @ B ) )
@ ( mexists_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [S2: mu] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
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: mu] :
( ( exists_in_world @ X12 @ X6 )
=> ( ~ ! [X14: mu] :
( ( exists_in_world @ X14 @ X6 )
=> ~ ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ! [X18: mu] :
( ( exists_in_world @ X18 @ X16 )
=> ( ( in @ X10 @ X12 @ X18 @ X16 )
| ~ ( do @ X8 @ X14 @ X18 @ X16 ) ) ) ) )
| ~ ( string @ X10 @ X6 )
| ~ ( entry_box @ X12 @ X6 ) ) ) ) ) ) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( ( (~)
@ ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y6 ) )
| ( !!
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y3 @ Y4 @ Y7 @ Y6 )
| ( (~) @ ( do @ Y2 @ Y5 @ Y7 @ Y6 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y3 @ Y1 ) )
| ( (~) @ ( entry_box @ Y4 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_3]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ( (~)
@ ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y5 ) )
| ( !!
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y2 @ Y3 @ Y6 @ Y5 )
| ( (~) @ ( do @ Y1 @ Y4 @ Y6 @ Y5 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y2 @ Y0 ) )
| ( (~) @ ( entry_box @ Y3 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl81,plain,
! [X2: $i,X4: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X4 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ( (~) @ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y1 @ X4 ) )
| ( (~) @ ( entry_box @ Y2 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl80]) ).
thf(zip_derived_cl82,plain,
! [X2: $i,X4: $i] :
( ~ ( rel_s4 @ X2 @ X4 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y1 @ Y2 @ Y5 @ Y4 )
| ( (~) @ ( do @ Y0 @ Y3 @ Y5 @ Y4 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y1 @ X4 ) )
| ( (~) @ ( entry_box @ Y2 @ X4 ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl81]) ).
thf(zip_derived_cl83,plain,
! [X2: $i,X4: $i,X6: mu] :
( ( ( exists_in_world @ X6 @ X4 )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ Y0 @ Y1 @ Y4 @ Y3 )
| ( (~) @ ( do @ X6 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y0 @ X4 ) )
| ( (~) @ ( entry_box @ Y1 @ X4 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl82]) ).
thf(zip_derived_cl84,plain,
! [X2: $i,X4: $i,X6: mu] :
( ~ ( exists_in_world @ X6 @ X4 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ Y0 @ Y1 @ Y4 @ Y3 )
| ( (~) @ ( do @ X6 @ Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ Y0 @ X4 ) )
| ( (~) @ ( entry_box @ Y1 @ X4 ) ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl83]) ).
thf(zip_derived_cl85,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu] :
( ( ( exists_in_world @ X8 @ X4 )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X8 @ Y0 @ Y3 @ Y2 )
| ( (~) @ ( do @ X6 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ X8 @ X4 ) )
| ( (~) @ ( entry_box @ Y0 @ X4 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl86,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu] :
( ~ ( exists_in_world @ X8 @ X4 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X8 @ Y0 @ Y3 @ Y2 )
| ( (~) @ ( do @ X6 @ Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ X8 @ X4 ) )
| ( (~) @ ( entry_box @ Y0 @ X4 ) ) ) ) )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl87,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ( ( exists_in_world @ X10 @ X4 )
=> ( ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X8 @ X10 @ Y2 @ Y1 )
| ( (~) @ ( do @ X6 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ X8 @ X4 ) )
| ( (~) @ ( entry_box @ X10 @ X4 ) ) ) )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl86]) ).
thf(zip_derived_cl88,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ~ ( exists_in_world @ X10 @ X4 )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X8 @ X10 @ Y2 @ Y1 )
| ( (~) @ ( do @ X6 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ( (~) @ ( string @ X8 @ X4 ) )
| ( (~) @ ( entry_box @ X10 @ X4 ) )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl87]) ).
thf(zip_derived_cl89,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X8 @ X10 @ Y2 @ Y1 )
| ( (~) @ ( do @ X6 @ Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( string @ X8 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X10 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl88]) ).
thf(zip_derived_cl90,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ~ ( ( exists_in_world @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X4 )
=> ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X8 @ X10 @ Y1 @ Y0 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X10 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( string @ X8 @ X4 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl91,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ( exists_in_world @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X4 )
| ~ ( string @ X8 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl137,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( exists_in_world @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X0 )
| ~ ( exists_in_world @ X3 @ X0 )
| ~ ( entry_box @ X1 @ X0 )
| ~ ( string @ X2 @ X0 )
| ( exists_in_world @ ( '#sk9' @ X0 @ X3 @ X2 @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl91]) ).
thf(zip_derived_cl31,plain,
! [X2: $i,X4: $i] :
( ( number @ ( '#sk2' @ X2 ) @ one @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl10_003,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl42,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( userid @ u @ ( '#sk3' @ X4 ) @ X6 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( rel_s4 @ X4 @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl133,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( userid @ u @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl42]) ).
thf(con,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [I: mu] :
( mexists_ind
@ ^ [B: mu] :
( mexists_ind
@ ^ [A: mu] :
( mexists_ind
@ ^ [S: mu] :
( mand @ ( mbox_s4 @ ( mand @ ( userid @ u @ I ) @ ( mand @ ( entry_box @ B ) @ ( number @ B @ one ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [S2: mu] : ( mimplies @ ( do @ S @ A @ S2 ) @ ( in @ I @ B @ S2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_4,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ! [X12: mu] :
( ( exists_in_world @ X12 @ X6 )
=> ! [X14: mu] :
( ( exists_in_world @ X14 @ X6 )
=> ( ~ ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ! [X20: mu] :
( ( exists_in_world @ X20 @ X18 )
=> ( ( in @ X8 @ X10 @ X20 @ X18 )
| ~ ( do @ X14 @ X12 @ X20 @ X18 ) ) ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ~ ( ~ ( entry_box @ X10 @ X16 )
| ~ ( number @ X10 @ one @ X16 )
| ~ ( userid @ u @ X8 @ X16 ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_5,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ! [X8: mu] :
( ( exists_in_world @ X8 @ X6 )
=> ! [X10: mu] :
( ( exists_in_world @ X10 @ X6 )
=> ! [X12: mu] :
( ( exists_in_world @ X12 @ X6 )
=> ! [X14: mu] :
( ( exists_in_world @ X14 @ X6 )
=> ( ~ ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ! [X20: mu] :
( ( exists_in_world @ X20 @ X18 )
=> ( ( in @ X8 @ X10 @ X20 @ X18 )
| ~ ( do @ X14 @ X12 @ X20 @ X18 ) ) ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ~ ( ~ ( entry_box @ X10 @ X16 )
| ~ ( number @ X10 @ one @ X16 )
| ~ ( userid @ u @ X8 @ X16 ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_4]) ).
thf(zip_derived_cl9,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y1 )
=> ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y1 )
=> ( ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y6 ) )
| ( !!
@ ^ [Y7: mu] :
( ( exists_in_world @ Y7 @ Y6 )
=> ( ( in @ Y2 @ Y3 @ Y7 @ Y6 )
| ( (~) @ ( do @ Y5 @ Y4 @ Y7 @ Y6 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y6 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y3 @ Y6 ) )
| ( (~) @ ( number @ Y3 @ one @ Y6 ) )
| ( (~) @ ( userid @ u @ Y2 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl43,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk4' @ Y0 ) )
| ( (~)
@ ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y0 )
=> ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y5 ) )
| ( !!
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ( in @ Y1 @ Y2 @ Y6 @ Y5 )
| ( (~) @ ( do @ Y4 @ Y3 @ Y6 @ Y5 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y5 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y2 @ Y5 ) )
| ( (~) @ ( number @ Y2 @ one @ Y5 ) )
| ( (~) @ ( userid @ u @ Y1 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl44,plain,
~ ( ( (~) @ ( rel_s4 @ '#sk4' @ '#sk5' ) )
| ( (~)
@ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk5' )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ( (~) @ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y4 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y1 @ Y4 ) )
| ( (~) @ ( number @ Y1 @ one @ Y4 ) )
| ( (~) @ ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl46,plain,
( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk5' )
=> ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ( in @ Y0 @ Y1 @ Y5 @ Y4 )
| ( (~) @ ( do @ Y3 @ Y2 @ Y5 @ Y4 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y4 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y1 @ Y4 ) )
| ( (~) @ ( number @ Y1 @ one @ Y4 ) )
| ( (~) @ ( userid @ u @ Y0 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl47,plain,
! [X2: mu] :
( ( exists_in_world @ X2 @ '#sk5' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ X2 @ Y0 @ Y4 @ Y3 )
| ( (~) @ ( do @ Y2 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y3 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y0 @ Y3 ) )
| ( (~) @ ( number @ Y0 @ one @ Y3 ) )
| ( (~) @ ( userid @ u @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl48,plain,
! [X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk5' )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ( in @ X2 @ Y0 @ Y4 @ Y3 )
| ( (~) @ ( do @ Y2 @ Y1 @ Y4 @ Y3 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y3 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ Y0 @ Y3 ) )
| ( (~) @ ( number @ Y0 @ one @ Y3 ) )
| ( (~) @ ( userid @ u @ X2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl49,plain,
! [X2: mu,X4: mu] :
( ( ( exists_in_world @ X4 @ '#sk5' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X2 @ X4 @ Y3 @ Y2 )
| ( (~) @ ( do @ Y1 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y2 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y2 ) )
| ( (~) @ ( number @ X4 @ one @ Y2 ) )
| ( (~) @ ( userid @ u @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl50,plain,
! [X2: mu,X4: mu] :
( ~ ( exists_in_world @ X4 @ '#sk5' )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ( in @ X2 @ X4 @ Y3 @ Y2 )
| ( (~) @ ( do @ Y1 @ Y0 @ Y3 @ Y2 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y2 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y2 ) )
| ( (~) @ ( number @ X4 @ one @ Y2 ) )
| ( (~) @ ( userid @ u @ X2 @ Y2 ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl51,plain,
! [X2: mu,X4: mu,X6: mu] :
( ( ( exists_in_world @ X6 @ '#sk5' )
=> ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X2 @ X4 @ Y2 @ Y1 )
| ( (~) @ ( do @ Y0 @ X6 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y1 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y1 ) )
| ( (~) @ ( number @ X4 @ one @ Y1 ) )
| ( (~) @ ( userid @ u @ X2 @ Y1 ) ) ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl52,plain,
! [X2: mu,X4: mu,X6: mu] :
( ~ ( exists_in_world @ X6 @ '#sk5' )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( in @ X2 @ X4 @ Y2 @ Y1 )
| ( (~) @ ( do @ Y0 @ X6 @ Y2 @ Y1 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y1 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y1 ) )
| ( (~) @ ( number @ X4 @ one @ Y1 ) )
| ( (~) @ ( userid @ u @ X2 @ Y1 ) ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl53,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( ( exists_in_world @ X8 @ '#sk5' )
=> ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X2 @ X4 @ Y1 @ Y0 )
| ( (~) @ ( do @ X8 @ X6 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl54,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( exists_in_world @ X8 @ '#sk5' )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X2 @ X4 @ Y1 @ Y0 )
| ( (~) @ ( do @ X8 @ X6 @ Y1 @ Y0 ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl55,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X2 @ X4 @ Y1 @ Y0 )
| ( (~) @ ( do @ X8 @ X6 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl56,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( (~) @ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
=> ( ( in @ X2 @ X4 @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ( (~) @ ( do @ X8 @ X6 @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ) ) ) ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl58,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
=> ( ( in @ X2 @ X4 @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ( (~) @ ( do @ X8 @ X6 @ Y0 @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl60,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
=> ( ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ( (~) @ ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ) ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl63,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl66,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( (~) @ ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) ) ) ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl69,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl64,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ( (~) @ ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl67,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl71,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( (~) @ ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl74,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl45,plain,
rel_s4 @ '#sk4' @ '#sk5',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl68,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl72,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( (~) @ ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl76,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl92,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X4 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( in @ X8 @ X10 @ Y1 @ Y0 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ ( string @ X8 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl93,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i] :
( ( (~) @ ( rel_s4 @ X4 @ X12 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X12 )
=> ( ( in @ X8 @ X10 @ Y0 @ X12 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ Y0 @ X12 ) ) ) ) )
| ~ ( exists_in_world @ X10 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( string @ X8 @ X4 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl92]) ).
thf(zip_derived_cl94,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i] :
( ~ ( rel_s4 @ X4 @ X12 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X12 )
=> ( ( in @ X8 @ X10 @ Y0 @ X12 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ Y0 @ X12 ) ) ) ) )
| ~ ( string @ X8 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X10 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl93]) ).
thf(zip_derived_cl95,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i,X14: mu] :
( ( ( exists_in_world @ X14 @ X12 )
=> ( ( in @ X8 @ X10 @ X14 @ X12 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X14 @ X12 ) ) ) )
| ~ ( exists_in_world @ X10 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( string @ X8 @ X4 )
| ~ ( rel_s4 @ X4 @ X12 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl94]) ).
thf(zip_derived_cl96,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i,X14: mu] :
( ~ ( exists_in_world @ X14 @ X12 )
| ( in @ X8 @ X10 @ X14 @ X12 )
| ( (~) @ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X14 @ X12 ) )
| ~ ( rel_s4 @ X4 @ X12 )
| ~ ( string @ X8 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X10 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl95]) ).
thf(zip_derived_cl97,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i,X14: mu] :
( ( in @ X8 @ X10 @ X14 @ X12 )
| ~ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X14 @ X12 )
| ~ ( exists_in_world @ X10 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( string @ X8 @ X4 )
| ~ ( rel_s4 @ X4 @ X12 )
| ~ ( exists_in_world @ X14 @ X12 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl164,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i,X4: mu,X5: mu,X6: $i] :
( ~ ( exists_in_world @ X5 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( rel_s4 @ X6 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X1 @ X3 )
| ( in @ X2 @ X1 @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl76,zip_derived_cl97]) ).
thf(zip_derived_cl179,plain,
! [X0: mu,X1: mu,X2: mu,X3: mu,X4: mu] :
( ( in @ X2 @ X1 @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl164]) ).
thf(zip_derived_cl188,plain,
! [X0: mu,X1: mu,X2: mu,X3: mu,X4: mu] :
( ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ( in @ X2 @ X1 @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl179]) ).
thf(zip_derived_cl193,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference('sup+',[status(thm)],[zip_derived_cl74,zip_derived_cl188]) ).
thf(zip_derived_cl199,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl193]) ).
thf(zip_derived_cl211,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl199]) ).
thf(zip_derived_cl223,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl211]) ).
thf(zip_derived_cl57,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk5' @ Y0 ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ Y0 ) )
| ( (~) @ ( number @ X4 @ one @ Y0 ) )
| ( (~) @ ( userid @ u @ X2 @ Y0 ) ) ) ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl59,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( ( (~) @ ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~)
@ ( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) ) ) ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl61,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl238,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl223,zip_derived_cl61]) ).
thf(zip_derived_cl137_004,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( exists_in_world @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X0 )
| ~ ( exists_in_world @ X3 @ X0 )
| ~ ( entry_box @ X1 @ X0 )
| ~ ( string @ X2 @ X0 )
| ( exists_in_world @ ( '#sk9' @ X0 @ X3 @ X2 @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl91]) ).
thf(zip_derived_cl239,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl238,zip_derived_cl137]) ).
thf(zip_derived_cl240,plain,
! [X0: mu,X1: mu] :
( ~ ( string @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X0 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' ) ),
inference(condensation,[status(thm)],[zip_derived_cl239]) ).
thf(mtransitive,axiom,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ) ).
thf('18',plain,
( mtransitive
= ( ^ [R: $i > $i > $o] :
! [S: $i,T: $i,U: $i] :
( ( ( R @ S @ T )
& ( R @ T @ U ) )
=> ( R @ S @ U ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mtransitive]) ).
thf('19',plain,
( mtransitive
= ( ^ [V_1: $i > $i > $o] :
! [X4: $i,X6: $i,X8: $i] :
( ( ( V_1 @ X4 @ X6 )
& ( V_1 @ X6 @ X8 ) )
=> ( V_1 @ X4 @ X8 ) ) ) ),
define([status(thm)]) ).
thf(a2,axiom,
mtransitive @ rel_s4 ).
thf(zf_stmt_6,axiom,
! [X4: $i,X6: $i,X8: $i] :
( ( ( rel_s4 @ X6 @ X8 )
& ( rel_s4 @ X4 @ X6 ) )
=> ( rel_s4 @ X4 @ X8 ) ) ).
thf(zip_derived_cl2,plain,
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( !!
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y0 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y2 ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_6]) ).
thf(zip_derived_cl20,plain,
! [X2: $i] :
( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ X2 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y1 ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl21,plain,
! [X2: $i,X4: $i] :
( !!
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X4 @ Y0 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ Y0 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl22,plain,
! [X2: $i,X4: $i,X6: $i] :
( ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
=> ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl23,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( ( rel_s4 @ X4 @ X6 )
& ( rel_s4 @ X2 @ X4 ) )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl24,plain,
! [X2: $i,X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( rel_s4 @ X2 @ X4 )
| ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl244,plain,
! [X0: mu,X1: mu,X2: $i] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( entry_box @ X0 @ '#sk5' )
| ~ ( string @ X1 @ '#sk5' )
| ( rel_s4 @ X2 @ ( '#sk7' @ X1 @ X0 ) )
| ~ ( rel_s4 @ X2 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl240,zip_derived_cl24]) ).
thf(zip_derived_cl133_005,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( userid @ u @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl42]) ).
thf(zip_derived_cl31_006,plain,
! [X2: $i,X4: $i] :
( ( number @ ( '#sk2' @ X2 ) @ one @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl62,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl65,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl158,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( rel_s4 @ X0 @ ( '#sk7' @ X1 @ ( '#sk2' @ X0 ) ) )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X1 @ ( '#sk2' @ X0 ) @ X3 @ X2 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( userid @ u @ X1 @ ( '#sk7' @ X1 @ ( '#sk2' @ X0 ) ) )
| ~ ( entry_box @ ( '#sk2' @ X0 ) @ ( '#sk7' @ X1 @ ( '#sk2' @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl65]) ).
thf(zip_derived_cl32_007,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( userid @ u @ X1 @ ( '#sk7' @ X1 @ ( '#sk2' @ X0 ) ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ X1 @ ( '#sk2' @ X0 ) @ X3 @ X2 ) )
| ~ ( rel_s4 @ X0 @ ( '#sk7' @ X1 @ ( '#sk2' @ X0 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl158,zip_derived_cl32]) ).
thf(zip_derived_cl171,plain,
! [X0: $i,X1: $i,X2: mu,X3: mu] :
( ~ ( rel_s4 @ X1 @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( rel_s4 @ X0 @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X0 ) ) )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X0 ) @ X3 @ X2 ) )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl133,zip_derived_cl170]) ).
thf(zip_derived_cl173,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( rel_s4 @ X0 @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl257,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( rel_s4 @ X0 @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl244,zip_derived_cl173]) ).
thf(zip_derived_cl267,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( rel_s4 @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl257]) ).
thf(zip_derived_cl32_008,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl472,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( rel_s4 @ X0 @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl267,zip_derived_cl32]) ).
thf(zip_derived_cl129_009,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( string @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl41]) ).
thf(zip_derived_cl473,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( rel_s4 @ X0 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl472,zip_derived_cl129]) ).
thf(zip_derived_cl69_010,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl74_011,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl10_012,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl164_013,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i,X4: mu,X5: mu,X6: $i] :
( ~ ( exists_in_world @ X5 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( rel_s4 @ X6 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X1 @ X3 )
| ( in @ X2 @ X1 @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl76,zip_derived_cl97]) ).
thf(zip_derived_cl182,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu,X4: mu,X5: mu] :
( ( in @ X3 @ X2 @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ X1 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ X1 ) )
| ~ ( exists_in_world @ X2 @ X0 )
| ~ ( exists_in_world @ X3 @ X0 )
| ~ ( exists_in_world @ X1 @ X0 )
| ~ ( entry_box @ X2 @ X0 )
| ~ ( string @ X3 @ X0 )
| ~ ( rel_s4 @ X0 @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ X1 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ X1 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ X1 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X0 @ X1 @ X3 @ X2 ) @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X5 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl164]) ).
thf(zip_derived_cl431,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X1 @ X3 ) ),
inference('sup+',[status(thm)],[zip_derived_cl74,zip_derived_cl182]) ).
thf(zip_derived_cl437,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X1 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( string @ X2 @ X3 )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl431]) ).
thf(zip_derived_cl797,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X1 @ X3 ) ),
inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl437]) ).
thf(zip_derived_cl875,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X1 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( string @ X2 @ X3 )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl797]) ).
thf(zip_derived_cl1059,plain,
! [X0: mu,X1: $i] :
( ~ ( rel_s4 @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) )
| ~ ( string @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl473,zip_derived_cl875]) ).
thf(zip_derived_cl1172,plain,
! [X0: mu,X1: $i] :
( ~ ( entry_box @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X1 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( rel_s4 @ X1 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1059]) ).
thf(zip_derived_cl32_014,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl2805,plain,
! [X0: mu,X1: $i] :
( ~ ( rel_s4 @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) )
| ~ ( string @ ( '#sk3' @ X1 ) @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl1172,zip_derived_cl32]) ).
thf(zip_derived_cl129_015,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( string @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl41]) ).
thf(zip_derived_cl2806,plain,
! [X0: mu,X1: $i] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ X1 ) @ ( '#sk2' @ X1 ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X1 ) @ '#sk5' )
| ~ ( rel_s4 @ X1 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl2805,zip_derived_cl129]) ).
thf(zip_derived_cl137_016,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( exists_in_world @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X0 )
| ~ ( exists_in_world @ X3 @ X0 )
| ~ ( entry_box @ X1 @ X0 )
| ~ ( string @ X2 @ X0 )
| ( exists_in_world @ ( '#sk9' @ X0 @ X3 @ X2 @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl91]) ).
thf(zip_derived_cl2807,plain,
! [X0: $i,X1: mu] :
( ~ ( rel_s4 @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' ) ),
inference('sup+',[status(thm)],[zip_derived_cl2806,zip_derived_cl137]) ).
thf(zip_derived_cl2812,plain,
! [X0: $i,X1: mu] :
( ~ ( entry_box @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( rel_s4 @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl2807]) ).
thf(zip_derived_cl2817,plain,
! [X0: $i] :
( ~ ( entry_box @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( rel_s4 @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' ) ),
inference(condensation,[status(thm)],[zip_derived_cl2812]) ).
thf(zip_derived_cl32_017,plain,
! [X2: $i,X4: $i] :
( ( entry_box @ ( '#sk2' @ X2 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl2818,plain,
! [X0: $i] :
( ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( rel_s4 @ X0 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( string @ ( '#sk3' @ X0 ) @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl2817,zip_derived_cl32]) ).
thf(zip_derived_cl129_018,plain,
! [X0: $i,X1: $i] :
( ~ ( rel_s4 @ X0 @ X1 )
| ( string @ ( '#sk3' @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl41]) ).
thf(zip_derived_cl2819,plain,
! [X0: $i] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) )
| ~ ( rel_s4 @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl2818,zip_derived_cl129]) ).
thf(zip_derived_cl173_019,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( rel_s4 @ X0 @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl2821,plain,
! [X0: mu,X1: mu] :
( ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) @ X1 @ X0 ) )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2819,zip_derived_cl173]) ).
thf(zip_derived_cl10_020,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl37,plain,
! [X2: $i,X4: $i] :
( ( exists_in_world @ ( '#sk3' @ X4 ) @ X4 )
| ~ ( rel_s4 @ X2 @ X4 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl99,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl10_021,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl99_022,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_023,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl2835,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) @ X1 @ X0 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl2821,zip_derived_cl99,zip_derived_cl27,zip_derived_cl10,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl70,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl73,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ( exists_in_world @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl75,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) )
| ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl78,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( in @ X2 @ X4 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl75]) ).
thf(zip_derived_cl45_024,plain,
rel_s4 @ '#sk4' @ '#sk5',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl77,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ( (~) @ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) ) )
| ( (~) @ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) ) )
| ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl72]) ).
thf(zip_derived_cl79,plain,
! [X2: mu,X4: mu,X6: mu,X8: mu] :
( ~ ( entry_box @ X4 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( number @ X4 @ one @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X6 @ '#sk5' )
| ~ ( exists_in_world @ X8 @ '#sk5' )
| ( do @ X8 @ X6 @ ( '#sk8' @ X2 @ X4 @ X6 @ X8 ) @ ( '#sk6' @ X2 @ X4 @ X6 @ X8 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl77]) ).
thf(zip_derived_cl97_025,plain,
! [X2: $i,X4: $i,X6: mu,X8: mu,X10: mu,X12: $i,X14: mu] :
( ( in @ X8 @ X10 @ X14 @ X12 )
| ~ ( do @ X6 @ ( '#sk9' @ X4 @ X6 @ X8 @ X10 ) @ X14 @ X12 )
| ~ ( exists_in_world @ X10 @ X4 )
| ~ ( exists_in_world @ X8 @ X4 )
| ~ ( exists_in_world @ X6 @ X4 )
| ~ ( rel_s4 @ X2 @ X4 )
| ~ ( entry_box @ X10 @ X4 )
| ~ ( string @ X8 @ X4 )
| ~ ( rel_s4 @ X4 @ X12 )
| ~ ( exists_in_world @ X14 @ X12 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl96]) ).
thf(zip_derived_cl175,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i,X4: mu,X5: mu,X6: $i] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X5 @ '#sk5' )
| ~ ( userid @ u @ X5 @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( number @ X4 @ one @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( entry_box @ X4 @ ( '#sk7' @ X5 @ X4 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( rel_s4 @ X6 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X1 @ X3 )
| ( in @ X2 @ X1 @ ( '#sk8' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X5 @ X4 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl97]) ).
thf(zip_derived_cl291,plain,
! [X0: mu,X1: mu,X2: mu,X3: mu,X4: mu] :
( ( in @ X2 @ X1 @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( entry_box @ X3 @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( number @ X3 @ one @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( userid @ u @ X4 @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl175]) ).
thf(zip_derived_cl305,plain,
! [X0: mu,X1: mu,X2: mu,X3: mu,X4: mu] :
( ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X3 @ '#sk5' )
| ~ ( exists_in_world @ X4 @ '#sk5' )
| ~ ( userid @ u @ X4 @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( number @ X3 @ one @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( entry_box @ X3 @ ( '#sk7' @ X4 @ X3 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ( in @ X2 @ X1 @ ( '#sk8' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X4 @ X3 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl291]) ).
thf(zip_derived_cl1689,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' ) ),
inference('sup+',[status(thm)],[zip_derived_cl78,zip_derived_cl305]) ).
thf(zip_derived_cl1695,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ ( '#sk8' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1689]) ).
thf(zip_derived_cl4643,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl1695]) ).
thf(zip_derived_cl4757,plain,
! [X0: mu,X1: mu,X2: mu] :
( ~ ( rel_s4 @ '#sk5' @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ X0 ) )
| ~ ( string @ X2 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ~ ( entry_box @ X1 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( number @ X1 @ one @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( userid @ u @ X2 @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl4643]) ).
thf(zip_derived_cl5053,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( userid @ u @ ( '#sk3' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( number @ ( '#sk2' @ '#sk5' ) @ one @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2835,zip_derived_cl4757]) ).
thf(zip_derived_cl99_026,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_027,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl5223,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( userid @ u @ ( '#sk3' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( number @ ( '#sk2' @ '#sk5' ) @ one @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl5053,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl5224,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( number @ ( '#sk2' @ '#sk5' ) @ one @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( userid @ u @ ( '#sk3' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl5223]) ).
thf(zip_derived_cl5575,plain,
! [X0: mu] :
( ~ ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( number @ ( '#sk2' @ '#sk5' ) @ one @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl133,zip_derived_cl5224]) ).
thf(zip_derived_cl99_028,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl45_029,plain,
rel_s4 @ '#sk4' @ '#sk5',
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
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_cl15,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_cl16,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_cl15]) ).
thf(zip_derived_cl17,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_cl16]) ).
thf(zip_derived_cl18,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_cl17]) ).
thf(zip_derived_cl19,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_cl18]) ).
thf(zip_derived_cl102,plain,
! [X0: mu] :
( ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk4' ) ),
inference('sup-',[status(thm)],[zip_derived_cl45,zip_derived_cl19]) ).
thf(zip_derived_cl106,plain,
exists_in_world @ ( '#sk3' @ '#sk4' ) @ '#sk5',
inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl102]) ).
thf(zip_derived_cl137_030,plain,
! [X0: $i,X1: mu,X2: mu,X3: mu] :
( ~ ( exists_in_world @ X1 @ X0 )
| ~ ( exists_in_world @ X2 @ X0 )
| ~ ( exists_in_world @ X3 @ X0 )
| ~ ( entry_box @ X1 @ X0 )
| ~ ( string @ X2 @ X0 )
| ( exists_in_world @ ( '#sk9' @ X0 @ X3 @ X2 @ X1 ) @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl91]) ).
thf(zip_derived_cl240_031,plain,
! [X0: mu,X1: mu] :
( ~ ( string @ X0 @ '#sk5' )
| ~ ( entry_box @ X1 @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X0 @ X1 ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' ) ),
inference(condensation,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl173_032,plain,
! [X0: $i,X1: mu,X2: mu] :
( ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ X0 ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ X0 ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) @ X2 @ X1 ) )
| ~ ( rel_s4 @ X0 @ ( '#sk7' @ ( '#sk3' @ X0 ) @ ( '#sk2' @ X0 ) ) ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl171]) ).
thf(zip_derived_cl241,plain,
! [X0: mu,X1: mu] :
( ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) @ X1 @ X0 ) )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl240,zip_derived_cl173]) ).
thf(zip_derived_cl27_033,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl99_034,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl99_035,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_036,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl251,plain,
! [X0: mu,X1: mu] :
( ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk6' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) @ X1 @ X0 ) )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl241,zip_derived_cl27,zip_derived_cl99,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl875_037,plain,
! [X0: mu,X1: mu,X2: mu,X3: $i] :
( ~ ( exists_in_world @ X1 @ X3 )
| ~ ( exists_in_world @ X2 @ X3 )
| ~ ( exists_in_world @ X0 @ X3 )
| ~ ( entry_box @ X1 @ X3 )
| ~ ( string @ X2 @ X3 )
| ~ ( rel_s4 @ X3 @ ( '#sk6' @ X2 @ X1 @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ X0 ) )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ X2 @ X1 ) )
| ~ ( exists_in_world @ X2 @ '#sk5' )
| ~ ( exists_in_world @ X1 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ X3 @ X0 @ X2 @ X1 ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl797]) ).
thf(zip_derived_cl1058,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl251,zip_derived_cl875]) ).
thf(zip_derived_cl27_038,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl99_039,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl99_040,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_041,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl1170,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl1058,zip_derived_cl27,zip_derived_cl99,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl1171,plain,
! [X0: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1170]) ).
thf(zip_derived_cl1375,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl137,zip_derived_cl1171]) ).
thf(zip_derived_cl99_042,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_043,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl1378,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl1375,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl1379,plain,
! [X0: mu] :
( ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1378]) ).
thf(zip_derived_cl1388,plain,
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl1379]) ).
thf(zip_derived_cl5577,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( number @ ( '#sk2' @ '#sk5' ) @ one @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl5575,zip_derived_cl1388]) ).
thf(zip_derived_cl5578,plain,
! [X0: mu] :
( ~ ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl31,zip_derived_cl5577]) ).
thf(zip_derived_cl1388_044,plain,
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl1379]) ).
thf(zip_derived_cl5580,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ ( '#sk9' @ '#sk5' @ X0 @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl5578,zip_derived_cl1388]) ).
thf(zip_derived_cl5582,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl137,zip_derived_cl5580]) ).
thf(zip_derived_cl99_045,plain,
! [X0: $i] : ( exists_in_world @ ( '#sk3' @ X0 ) @ X0 ),
inference('sup-',[status(thm)],[zip_derived_cl10,zip_derived_cl37]) ).
thf(zip_derived_cl27_046,plain,
! [X2: $i] : ( exists_in_world @ ( '#sk2' @ X2 ) @ X2 ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl5585,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl5582,zip_derived_cl99,zip_derived_cl27]) ).
thf(zip_derived_cl5586,plain,
! [X0: mu] :
( ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference(simplify,[status(thm)],[zip_derived_cl5585]) ).
thf(zip_derived_cl5593,plain,
! [X0: mu] :
( ~ ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl5586]) ).
thf(zip_derived_cl1388_047,plain,
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ( rel_s4 @ '#sk5' @ ( '#sk7' @ ( '#sk3' @ '#sk5' ) @ ( '#sk2' @ '#sk5' ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl1379]) ).
thf(zip_derived_cl5595,plain,
! [X0: mu] :
( ~ ( exists_in_world @ X0 @ '#sk5' )
| ~ ( entry_box @ ( '#sk2' @ '#sk5' ) @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' ) ),
inference(clc,[status(thm)],[zip_derived_cl5593,zip_derived_cl1388]) ).
thf(zip_derived_cl5596,plain,
! [X0: mu] :
( ~ ( rel_s4 @ '#sk5' @ '#sk5' )
| ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl32,zip_derived_cl5595]) ).
thf(zip_derived_cl10_048,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5598,plain,
! [X0: mu] :
( ~ ( string @ ( '#sk3' @ '#sk5' ) @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference(demod,[status(thm)],[zip_derived_cl5596,zip_derived_cl10]) ).
thf(zip_derived_cl5600,plain,
! [X0: mu] :
( ~ ( rel_s4 @ '#sk5' @ '#sk5' )
| ~ ( exists_in_world @ X0 @ '#sk5' ) ),
inference('sup-',[status(thm)],[zip_derived_cl129,zip_derived_cl5598]) ).
thf(zip_derived_cl10_049,plain,
! [X2: $i] : ( rel_s4 @ X2 @ X2 ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl5602,plain,
! [X0: mu] :
~ ( exists_in_world @ X0 @ '#sk5' ),
inference(demod,[status(thm)],[zip_derived_cl5600,zip_derived_cl10]) ).
thf(zip_derived_cl106_050,plain,
exists_in_world @ ( '#sk3' @ '#sk4' ) @ '#sk5',
inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl102]) ).
thf(zip_derived_cl5606,plain,
$false,
inference('sup+',[status(thm)],[zip_derived_cl5602,zip_derived_cl106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : KRS272^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6pP51py24J true
% 0.14/0.35 % Computer : n001.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 : Mon Aug 28 02:29:49 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
% 0.14/0.35 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in HO mode
% 0.22/0.67 % Total configuration time : 828
% 0.22/0.67 % Estimated wc time : 1656
% 0.22/0.67 % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 1.13/0.77 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 1.13/0.77 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 1.13/0.77 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 1.13/0.78 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 1.13/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 1.13/0.78 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.13/0.80 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 1.43/0.90 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 41.70/5.96 % Solved by lams/30_sp5.sh.
% 41.70/5.96 % done 1700 iterations in 5.107s
% 41.70/5.96 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 41.70/5.96 % SZS output start Refutation
% See solution above
% 41.70/5.97
% 41.70/5.97
% 41.70/5.97 % Terminating...
% 42.25/6.10 % Runner terminated.
% 42.25/6.11 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------