TSTP Solution File: SWV097^7 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWV097^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TxONrwWHQW true
% Computer : n014.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 : Fri Sep 1 00:07:39 EDT 2023
% Result : Theorem 28.75s 4.37s
% Output : Refutation 29.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 96
% Number of leaves : 255
% Syntax : Number of formulae : 1097 ( 216 unt; 110 typ; 0 def)
% Number of atoms : 25824 ( 21 equ;6947 cnn)
% Maximal formula atoms : 475 ( 26 avg)
% Number of connectives : 76946 (12305 ~;11925 |; 0 &;47053 @)
% ( 0 <=>; 547 =>; 0 <=; 0 <~>)
% Maximal formula depth : 54 ( 14 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 109 usr; 91 con; 0-3 aty)
% (5116 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 5985 (5166 ^; 819 !; 0 ?;5985 :)
% Comments :
%------------------------------------------------------------------------------
thf(mu_type,type,
mu: $tType ).
thf('#sk3_type',type,
'#sk3': $i ).
thf(rho_defuse_type,type,
rho_defuse: mu ).
thf('#sk1_type',type,
'#sk1': $i ).
thf('#sk34_type',type,
'#sk34': $i ).
thf('#form40_type',type,
'#form40': $o ).
thf('#sk79_type',type,
'#sk79': $i ).
thf('#sk45_type',type,
'#sk45': $i ).
thf('#sk76_type',type,
'#sk76': $i ).
thf('#form27_type',type,
'#form27': $o ).
thf('#form62_type',type,
'#form62': $o ).
thf(use_type,type,
use: mu ).
thf('#sk22_type',type,
'#sk22': $i ).
thf('#sk69_type',type,
'#sk69': mu ).
thf('#sk71_type',type,
'#sk71': $i ).
thf(u_defuse_type,type,
u_defuse: mu ).
thf(xinit_noise_defuse_type,type,
xinit_noise_defuse: mu ).
thf('#form46_type',type,
'#form46': $o ).
thf('#sk49_type',type,
'#sk49': $i ).
thf('#form35_type',type,
'#form35': mu > mu > $i > $o ).
thf('#sk8_type',type,
'#sk8': $i ).
thf(a_select2_type,type,
a_select2: mu > mu > mu ).
thf('#sk32_type',type,
'#sk32': mu > $i > $i ).
thf('#form36_type',type,
'#form36': $o ).
thf(rel_s4_type,type,
rel_s4: $i > $i > $o ).
thf('#sk10_type',type,
'#sk10': $i ).
thf('#form58_type',type,
'#form58': $o ).
thf('#sk31_type',type,
'#sk31': $i ).
thf('#sk2_type',type,
'#sk2': $i ).
thf('#form60_type',type,
'#form60': $o ).
thf('#form52_type',type,
'#form52': $o ).
thf('#form54_type',type,
'#form54': $o ).
thf(minus_type,type,
minus: mu > mu > mu ).
thf(mforall_ind_type,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(a_select3_type,type,
a_select3: mu > mu > mu > mu ).
thf('#form13_type',type,
'#form13': $o ).
thf('#sk53_type',type,
'#sk53': $i ).
thf('#form56_type',type,
'#form56': $o ).
thf('#form50_type',type,
'#form50': $o ).
thf(mnot_type,type,
mnot: ( $i > $o ) > $i > $o ).
thf(mor_type,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form17_type',type,
'#form17': $o ).
thf('#sk66_type',type,
'#sk66': mu ).
thf('#sk47_type',type,
'#sk47': $i ).
thf(n2_type,type,
n2: mu ).
thf('#form33_type',type,
'#form33': $o ).
thf('#form23_type',type,
'#form23': $o ).
thf(pv5_type,type,
pv5: mu ).
thf('#form25_type',type,
'#form25': mu > $i > $o ).
thf('#sk43_type',type,
'#sk43': $i ).
thf(n1_type,type,
n1: mu ).
thf(n5_type,type,
n5: mu ).
thf('#sk16_type',type,
'#sk16': $i ).
thf('#sk39_type',type,
'#sk39': $i ).
thf('#sk75_type',type,
'#sk75': $i ).
thf('#sk28_type',type,
'#sk28': $i ).
thf('#sk78_type',type,
'#sk78': $i ).
thf('#sk24_type',type,
'#sk24': $i ).
thf('#sk65_type',type,
'#sk65': $i ).
thf('#sk63_type',type,
'#sk63': $i ).
thf(sigma_defuse_type,type,
sigma_defuse: mu ).
thf('#form11_type',type,
'#form11': $o ).
thf(z_defuse_type,type,
z_defuse: mu ).
thf('#form21_type',type,
'#form21': $o ).
thf('#sk55_type',type,
'#sk55': $i ).
thf('#sk37_type',type,
'#sk37': $i ).
thf(mimplies_type,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#form64_type',type,
'#form64': $o ).
thf('#form15_type',type,
'#form15': $o ).
thf('#sk73_type',type,
'#sk73': mu ).
thf('#form19_type',type,
'#form19': mu > $i > $o ).
thf('#sk14_type',type,
'#sk14': $i ).
thf('#form48_type',type,
'#form48': $o ).
thf('#form44_type',type,
'#form44': $o ).
thf(xinit_mean_defuse_type,type,
xinit_mean_defuse: mu ).
thf('#form67_type',type,
'#form67': $o ).
thf(mbox_s4_type,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf('#sk20_type',type,
'#sk20': mu > $i > $i ).
thf(exists_in_world_type,type,
exists_in_world: mu > $i > $o ).
thf('#sk72_type',type,
'#sk72': mu ).
thf(qmltpeq_type,type,
qmltpeq: mu > mu > $i > $o ).
thf(n0_type,type,
n0: mu ).
thf('#sk59_type',type,
'#sk59': $i ).
thf('#sk77_type',type,
'#sk77': $i ).
thf(n4_type,type,
n4: mu ).
thf('#form30_type',type,
'#form30': $o ).
thf('#sk26_type',type,
'#sk26': mu > $i > $i ).
thf('#form9_type',type,
'#form9': $o ).
thf('#sk61_type',type,
'#sk61': $i ).
thf(n999_type,type,
n999: mu ).
thf('#form38_type',type,
'#form38': $o ).
thf('#sk41_type',type,
'#sk41': $i ).
thf(xinit_defuse_type,type,
xinit_defuse: mu ).
thf(leq_type,type,
leq: mu > mu > $i > $o ).
thf('#sk4_type',type,
'#sk4': $i ).
thf('#sk70_type',type,
'#sk70': $i ).
thf('#sk6_type',type,
'#sk6': $i ).
thf(mand_type,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf('#sk68_type',type,
'#sk68': $i ).
thf('#sk12_type',type,
'#sk12': $i ).
thf('#sk18_type',type,
'#sk18': $i ).
thf('#sk74_type',type,
'#sk74': $i ).
thf('#sk29_type',type,
'#sk29': mu > $i > $i ).
thf('#sk57_type',type,
'#sk57': $i ).
thf(n3_type,type,
n3: mu ).
thf(mvalid_type,type,
mvalid: ( $i > $o ) > $o ).
thf('#sk51_type',type,
'#sk51': $i ).
thf('#form42_type',type,
'#form42': $o ).
thf('#form5_type',type,
'#form5': $o ).
thf('#form7_type',type,
'#form7': $o ).
thf(mbox_s4,axiom,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ) ).
thf('0',plain,
( mbox_s4
= ( ^ [Phi: $i > $o,W: $i] :
! [V: $i] :
( ( Phi @ V )
| ~ ( rel_s4 @ W @ V ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mbox_s4]) ).
thf('1',plain,
( mbox_s4
= ( ^ [V_1: $i > $o,V_2: $i] :
! [X4: $i] :
( ( V_1 @ X4 )
| ~ ( rel_s4 @ V_2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ) ).
thf('2',plain,
( mvalid
= ( ^ [Phi: $i > $o] :
! [W: $i] : ( Phi @ W ) ) ),
inference(simplify_rw_rule,[status(thm)],[mvalid]) ).
thf('3',plain,
( mvalid
= ( ^ [V_1: $i > $o] :
! [X4: $i] : ( V_1 @ X4 ) ) ),
define([status(thm)]) ).
thf(mforall_ind,axiom,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ) ).
thf('4',plain,
( mforall_ind
= ( ^ [Phi: mu > $i > $o,W: $i] :
! [X: mu] :
( ( exists_in_world @ X @ W )
=> ( Phi @ X @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mforall_ind]) ).
thf('5',plain,
( mforall_ind
= ( ^ [V_1: mu > $i > $o,V_2: $i] :
! [X4: mu] :
( ( exists_in_world @ X4 @ V_2 )
=> ( V_1 @ X4 @ V_2 ) ) ) ),
define([status(thm)]) ).
thf(mimplies,axiom,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ) ).
thf(mor,axiom,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ) ).
thf('6',plain,
( mor
= ( ^ [Phi: $i > $o,Psi: $i > $o,W: $i] :
( ( Phi @ W )
| ( Psi @ W ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mor]) ).
thf('7',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(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,
( mimplies
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mor @ ( mnot @ Phi ) @ Psi ) ) ),
inference(simplify_rw_rule,[status(thm)],[mimplies,'7','9']) ).
thf('11',plain,
( mimplies
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mor @ ( mnot @ V_1 ) @ V_2 ) ) ),
define([status(thm)]) ).
thf(mand,axiom,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ) ).
thf('12',plain,
( mand
= ( ^ [Phi: $i > $o,Psi: $i > $o] : ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) ) ),
inference(simplify_rw_rule,[status(thm)],[mand,'7','9']) ).
thf('13',plain,
( mand
= ( ^ [V_1: $i > $o,V_2: $i > $o] : ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) ) ),
define([status(thm)]) ).
thf(quaternion_ds1_inuse_0009,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv5 ) )
@ ( mand @ ( mbox_s4 @ ( leq @ pv5 @ ( minus @ n999 @ n1 ) ) )
@ ( mand
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ A ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ B ) ) @ ( mand @ ( mbox_s4 @ ( leq @ A @ n2 ) ) @ ( mbox_s4 @ ( leq @ B @ pv5 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ A @ B ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ A @ B ) @ use ) ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [D: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ C ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ D ) ) @ ( mand @ ( mbox_s4 @ ( leq @ C @ n2 ) ) @ ( mbox_s4 @ ( leq @ D @ ( minus @ pv5 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ C @ D ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ C @ D ) @ use ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use ) )
@ ( mand @ ( mbox_s4 @ ( leq @ n0 @ pv5 ) )
@ ( mand @ ( mbox_s4 @ ( leq @ pv5 @ ( minus @ n999 @ n1 ) ) )
@ ( mand
@ ( mbox_s4
@ ( mforall_ind
@ ^ [E: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [F: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ E ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ F ) ) @ ( mand @ ( mbox_s4 @ ( leq @ E @ n2 ) ) @ ( mbox_s4 @ ( leq @ F @ pv5 ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ E @ F ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ E @ F ) @ use ) ) ) ) ) ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [G: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [H: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ G ) ) @ ( mand @ ( mbox_s4 @ ( leq @ n0 @ H ) ) @ ( mand @ ( mbox_s4 @ ( leq @ G @ n2 ) ) @ ( mbox_s4 @ ( leq @ H @ ( minus @ pv5 @ n1 ) ) ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ u_defuse @ G @ H ) @ use ) ) @ ( mbox_s4 @ ( qmltpeq @ ( a_select3 @ z_defuse @ G @ H ) @ use ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,conjecture,
! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ! [X112: $i] :
( ~ ( rel_s4 @ X6 @ X112 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X112 ) )
| ~ ! [X116: $i] :
( ~ ( rel_s4 @ X6 @ X116 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X116 ) )
| ~ ! [X120: $i] :
( ~ ( rel_s4 @ X6 @ X120 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X120 ) )
| ~ ! [X124: $i] :
( ~ ( rel_s4 @ X6 @ X124 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X124 ) )
| ~ ! [X128: $i] :
( ~ ( rel_s4 @ X6 @ X128 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X128 ) )
| ~ ! [X132: $i] :
( ~ ( rel_s4 @ X6 @ X132 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X132 ) )
| ~ ! [X136: $i] :
( ~ ( rel_s4 @ X6 @ X136 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X136 ) )
| ~ ! [X140: $i] :
( ~ ( rel_s4 @ X6 @ X140 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X140 ) )
| ~ ! [X144: $i] :
( ~ ( rel_s4 @ X6 @ X144 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X144 ) )
| ~ ! [X148: $i] :
( ~ ( rel_s4 @ X6 @ X148 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X148 ) )
| ~ ! [X152: $i] :
( ~ ( rel_s4 @ X6 @ X152 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X152 ) )
| ~ ! [X156: $i] :
( ~ ( rel_s4 @ X6 @ X156 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X156 ) )
| ~ ! [X160: $i] :
( ~ ( rel_s4 @ X6 @ X160 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X160 ) )
| ~ ! [X164: $i] :
( ~ ( rel_s4 @ X6 @ X164 )
| ( leq @ n0 @ pv5 @ X164 ) )
| ~ ! [X168: $i] :
( ~ ( rel_s4 @ X6 @ X168 )
| ! [X170: mu] :
( ( exists_in_world @ X170 @ X168 )
=> ! [X172: $i] :
( ~ ( rel_s4 @ X168 @ X172 )
| ! [X174: mu] :
( ( exists_in_world @ X174 @ X172 )
=> ! [X176: $i] :
( ~ ( rel_s4 @ X172 @ X176 )
| ~ ( ~ ! [X188: $i] :
( ~ ( rel_s4 @ X176 @ X188 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X170 @ X174 ) @ use @ X188 ) )
| ~ ! [X186: $i] :
( ~ ( rel_s4 @ X176 @ X186 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X170 @ X174 ) @ use @ X186 ) ) )
| ~ ! [X178: $i] :
( ~ ( rel_s4 @ X176 @ X178 )
| ( leq @ n0 @ X170 @ X178 ) )
| ~ ! [X182: $i] :
( ~ ( rel_s4 @ X176 @ X182 )
| ( leq @ X170 @ n2 @ X182 ) )
| ~ ! [X184: $i] :
( ~ ( rel_s4 @ X176 @ X184 )
| ( leq @ X174 @ pv5 @ X184 ) )
| ~ ! [X180: $i] :
( ~ ( rel_s4 @ X176 @ X180 )
| ( leq @ n0 @ X174 @ X180 ) ) ) ) ) ) )
| ~ ! [X190: $i] :
( ~ ( rel_s4 @ X6 @ X190 )
| ! [X192: mu] :
( ( exists_in_world @ X192 @ X190 )
=> ! [X194: $i] :
( ~ ( rel_s4 @ X190 @ X194 )
| ! [X196: mu] :
( ( exists_in_world @ X196 @ X194 )
=> ! [X198: $i] :
( ~ ( rel_s4 @ X194 @ X198 )
| ~ ( ~ ! [X210: $i] :
( ~ ( rel_s4 @ X198 @ X210 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X192 @ X196 ) @ use @ X210 ) )
| ~ ! [X208: $i] :
( ~ ( rel_s4 @ X198 @ X208 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X192 @ X196 ) @ use @ X208 ) ) )
| ~ ! [X200: $i] :
( ~ ( rel_s4 @ X198 @ X200 )
| ( leq @ n0 @ X192 @ X200 ) )
| ~ ! [X204: $i] :
( ~ ( rel_s4 @ X198 @ X204 )
| ( leq @ X192 @ n2 @ X204 ) )
| ~ ! [X206: $i] :
( ~ ( rel_s4 @ X198 @ X206 )
| ( leq @ X196 @ ( minus @ pv5 @ n1 ) @ X206 ) )
| ~ ! [X202: $i] :
( ~ ( rel_s4 @ X198 @ X202 )
| ( leq @ n0 @ X196 @ X202 ) ) ) ) ) ) )
| ~ ! [X166: $i] :
( ~ ( rel_s4 @ X6 @ X166 )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X166 ) )
| ~ ! [X162: $i] :
( ~ ( rel_s4 @ X6 @ X162 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X162 ) )
| ~ ! [X158: $i] :
( ~ ( rel_s4 @ X6 @ X158 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X158 ) )
| ~ ! [X154: $i] :
( ~ ( rel_s4 @ X6 @ X154 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X154 ) )
| ~ ! [X150: $i] :
( ~ ( rel_s4 @ X6 @ X150 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X150 ) )
| ~ ! [X146: $i] :
( ~ ( rel_s4 @ X6 @ X146 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X146 ) )
| ~ ! [X142: $i] :
( ~ ( rel_s4 @ X6 @ X142 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X142 ) )
| ~ ! [X138: $i] :
( ~ ( rel_s4 @ X6 @ X138 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X138 ) )
| ~ ! [X134: $i] :
( ~ ( rel_s4 @ X6 @ X134 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X134 ) )
| ~ ! [X130: $i] :
( ~ ( rel_s4 @ X6 @ X130 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X130 ) )
| ~ ! [X126: $i] :
( ~ ( rel_s4 @ X6 @ X126 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X126 ) )
| ~ ! [X122: $i] :
( ~ ( rel_s4 @ X6 @ X122 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X122 ) )
| ~ ! [X118: $i] :
( ~ ( rel_s4 @ X6 @ X118 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X118 ) )
| ~ ! [X114: $i] :
( ~ ( rel_s4 @ X6 @ X114 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X114 ) )
| ~ ! [X110: $i] :
( ~ ( rel_s4 @ X6 @ X110 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X110 ) ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X8 ) )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X6 @ X12 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X12 ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X16 ) )
| ~ ! [X20: $i] :
( ~ ( rel_s4 @ X6 @ X20 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X20 ) )
| ~ ! [X24: $i] :
( ~ ( rel_s4 @ X6 @ X24 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X24 ) )
| ~ ! [X28: $i] :
( ~ ( rel_s4 @ X6 @ X28 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X28 ) )
| ~ ! [X32: $i] :
( ~ ( rel_s4 @ X6 @ X32 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X32 ) )
| ~ ! [X36: $i] :
( ~ ( rel_s4 @ X6 @ X36 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X36 ) )
| ~ ! [X40: $i] :
( ~ ( rel_s4 @ X6 @ X40 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X40 ) )
| ~ ! [X44: $i] :
( ~ ( rel_s4 @ X6 @ X44 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X44 ) )
| ~ ! [X48: $i] :
( ~ ( rel_s4 @ X6 @ X48 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X48 ) )
| ~ ! [X52: $i] :
( ~ ( rel_s4 @ X6 @ X52 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X52 ) )
| ~ ! [X56: $i] :
( ~ ( rel_s4 @ X6 @ X56 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X56 ) )
| ~ ! [X60: $i] :
( ~ ( rel_s4 @ X6 @ X60 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X60 ) )
| ~ ! [X64: $i] :
( ~ ( rel_s4 @ X6 @ X64 )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X64 ) )
| ~ ! [X88: $i] :
( ~ ( rel_s4 @ X6 @ X88 )
| ! [X90: mu] :
( ( exists_in_world @ X90 @ X88 )
=> ! [X92: $i] :
( ~ ( rel_s4 @ X88 @ X92 )
| ! [X94: mu] :
( ( exists_in_world @ X94 @ X92 )
=> ! [X96: $i] :
( ~ ( rel_s4 @ X92 @ X96 )
| ~ ( ~ ! [X108: $i] :
( ~ ( rel_s4 @ X96 @ X108 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X90 @ X94 ) @ use @ X108 ) )
| ~ ! [X106: $i] :
( ~ ( rel_s4 @ X96 @ X106 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X90 @ X94 ) @ use @ X106 ) ) )
| ~ ! [X98: $i] :
( ~ ( rel_s4 @ X96 @ X98 )
| ( leq @ n0 @ X90 @ X98 ) )
| ~ ! [X102: $i] :
( ~ ( rel_s4 @ X96 @ X102 )
| ( leq @ X90 @ n2 @ X102 ) )
| ~ ! [X104: $i] :
( ~ ( rel_s4 @ X96 @ X104 )
| ( leq @ X94 @ ( minus @ pv5 @ n1 ) @ X104 ) )
| ~ ! [X100: $i] :
( ~ ( rel_s4 @ X96 @ X100 )
| ( leq @ n0 @ X94 @ X100 ) ) ) ) ) ) )
| ~ ! [X66: $i] :
( ~ ( rel_s4 @ X6 @ X66 )
| ! [X68: mu] :
( ( exists_in_world @ X68 @ X66 )
=> ! [X70: $i] :
( ~ ( rel_s4 @ X66 @ X70 )
| ! [X72: mu] :
( ( exists_in_world @ X72 @ X70 )
=> ! [X74: $i] :
( ~ ( rel_s4 @ X70 @ X74 )
| ~ ( ~ ! [X86: $i] :
( ~ ( rel_s4 @ X74 @ X86 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X68 @ X72 ) @ use @ X86 ) )
| ~ ! [X84: $i] :
( ~ ( rel_s4 @ X74 @ X84 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X68 @ X72 ) @ use @ X84 ) ) )
| ~ ! [X76: $i] :
( ~ ( rel_s4 @ X74 @ X76 )
| ( leq @ n0 @ X68 @ X76 ) )
| ~ ! [X80: $i] :
( ~ ( rel_s4 @ X74 @ X80 )
| ( leq @ X68 @ n2 @ X80 ) )
| ~ ! [X82: $i] :
( ~ ( rel_s4 @ X74 @ X82 )
| ( leq @ X72 @ pv5 @ X82 ) )
| ~ ! [X78: $i] :
( ~ ( rel_s4 @ X74 @ X78 )
| ( leq @ n0 @ X72 @ X78 ) ) ) ) ) ) )
| ~ ! [X62: $i] :
( ~ ( rel_s4 @ X6 @ X62 )
| ( leq @ n0 @ pv5 @ X62 ) )
| ~ ! [X58: $i] :
( ~ ( rel_s4 @ X6 @ X58 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X58 ) )
| ~ ! [X54: $i] :
( ~ ( rel_s4 @ X6 @ X54 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X54 ) )
| ~ ! [X50: $i] :
( ~ ( rel_s4 @ X6 @ X50 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X50 ) )
| ~ ! [X46: $i] :
( ~ ( rel_s4 @ X6 @ X46 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X46 ) )
| ~ ! [X42: $i] :
( ~ ( rel_s4 @ X6 @ X42 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X42 ) )
| ~ ! [X38: $i] :
( ~ ( rel_s4 @ X6 @ X38 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X38 ) )
| ~ ! [X34: $i] :
( ~ ( rel_s4 @ X6 @ X34 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X34 ) )
| ~ ! [X30: $i] :
( ~ ( rel_s4 @ X6 @ X30 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X30 ) )
| ~ ! [X26: $i] :
( ~ ( rel_s4 @ X6 @ X26 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X26 ) )
| ~ ! [X22: $i] :
( ~ ( rel_s4 @ X6 @ X22 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X22 ) )
| ~ ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X18 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X6 @ X14 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X14 ) )
| ~ ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X10 ) ) ) ).
thf(zf_stmt_1,negated_conjecture,
~ ! [X4: $i,X6: $i] :
( ~ ( rel_s4 @ X4 @ X6 )
| ~ ( ~ ! [X112: $i] :
( ~ ( rel_s4 @ X6 @ X112 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X112 ) )
| ~ ! [X116: $i] :
( ~ ( rel_s4 @ X6 @ X116 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X116 ) )
| ~ ! [X120: $i] :
( ~ ( rel_s4 @ X6 @ X120 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X120 ) )
| ~ ! [X124: $i] :
( ~ ( rel_s4 @ X6 @ X124 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X124 ) )
| ~ ! [X128: $i] :
( ~ ( rel_s4 @ X6 @ X128 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X128 ) )
| ~ ! [X132: $i] :
( ~ ( rel_s4 @ X6 @ X132 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X132 ) )
| ~ ! [X136: $i] :
( ~ ( rel_s4 @ X6 @ X136 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X136 ) )
| ~ ! [X140: $i] :
( ~ ( rel_s4 @ X6 @ X140 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X140 ) )
| ~ ! [X144: $i] :
( ~ ( rel_s4 @ X6 @ X144 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X144 ) )
| ~ ! [X148: $i] :
( ~ ( rel_s4 @ X6 @ X148 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X148 ) )
| ~ ! [X152: $i] :
( ~ ( rel_s4 @ X6 @ X152 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X152 ) )
| ~ ! [X156: $i] :
( ~ ( rel_s4 @ X6 @ X156 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X156 ) )
| ~ ! [X160: $i] :
( ~ ( rel_s4 @ X6 @ X160 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X160 ) )
| ~ ! [X164: $i] :
( ~ ( rel_s4 @ X6 @ X164 )
| ( leq @ n0 @ pv5 @ X164 ) )
| ~ ! [X168: $i] :
( ~ ( rel_s4 @ X6 @ X168 )
| ! [X170: mu] :
( ( exists_in_world @ X170 @ X168 )
=> ! [X172: $i] :
( ~ ( rel_s4 @ X168 @ X172 )
| ! [X174: mu] :
( ( exists_in_world @ X174 @ X172 )
=> ! [X176: $i] :
( ~ ( rel_s4 @ X172 @ X176 )
| ~ ( ~ ! [X188: $i] :
( ~ ( rel_s4 @ X176 @ X188 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X170 @ X174 ) @ use @ X188 ) )
| ~ ! [X186: $i] :
( ~ ( rel_s4 @ X176 @ X186 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X170 @ X174 ) @ use @ X186 ) ) )
| ~ ! [X178: $i] :
( ~ ( rel_s4 @ X176 @ X178 )
| ( leq @ n0 @ X170 @ X178 ) )
| ~ ! [X182: $i] :
( ~ ( rel_s4 @ X176 @ X182 )
| ( leq @ X170 @ n2 @ X182 ) )
| ~ ! [X184: $i] :
( ~ ( rel_s4 @ X176 @ X184 )
| ( leq @ X174 @ pv5 @ X184 ) )
| ~ ! [X180: $i] :
( ~ ( rel_s4 @ X176 @ X180 )
| ( leq @ n0 @ X174 @ X180 ) ) ) ) ) ) )
| ~ ! [X190: $i] :
( ~ ( rel_s4 @ X6 @ X190 )
| ! [X192: mu] :
( ( exists_in_world @ X192 @ X190 )
=> ! [X194: $i] :
( ~ ( rel_s4 @ X190 @ X194 )
| ! [X196: mu] :
( ( exists_in_world @ X196 @ X194 )
=> ! [X198: $i] :
( ~ ( rel_s4 @ X194 @ X198 )
| ~ ( ~ ! [X210: $i] :
( ~ ( rel_s4 @ X198 @ X210 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X192 @ X196 ) @ use @ X210 ) )
| ~ ! [X208: $i] :
( ~ ( rel_s4 @ X198 @ X208 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X192 @ X196 ) @ use @ X208 ) ) )
| ~ ! [X200: $i] :
( ~ ( rel_s4 @ X198 @ X200 )
| ( leq @ n0 @ X192 @ X200 ) )
| ~ ! [X204: $i] :
( ~ ( rel_s4 @ X198 @ X204 )
| ( leq @ X192 @ n2 @ X204 ) )
| ~ ! [X206: $i] :
( ~ ( rel_s4 @ X198 @ X206 )
| ( leq @ X196 @ ( minus @ pv5 @ n1 ) @ X206 ) )
| ~ ! [X202: $i] :
( ~ ( rel_s4 @ X198 @ X202 )
| ( leq @ n0 @ X196 @ X202 ) ) ) ) ) ) )
| ~ ! [X166: $i] :
( ~ ( rel_s4 @ X6 @ X166 )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X166 ) )
| ~ ! [X162: $i] :
( ~ ( rel_s4 @ X6 @ X162 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X162 ) )
| ~ ! [X158: $i] :
( ~ ( rel_s4 @ X6 @ X158 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X158 ) )
| ~ ! [X154: $i] :
( ~ ( rel_s4 @ X6 @ X154 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X154 ) )
| ~ ! [X150: $i] :
( ~ ( rel_s4 @ X6 @ X150 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X150 ) )
| ~ ! [X146: $i] :
( ~ ( rel_s4 @ X6 @ X146 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X146 ) )
| ~ ! [X142: $i] :
( ~ ( rel_s4 @ X6 @ X142 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X142 ) )
| ~ ! [X138: $i] :
( ~ ( rel_s4 @ X6 @ X138 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X138 ) )
| ~ ! [X134: $i] :
( ~ ( rel_s4 @ X6 @ X134 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X134 ) )
| ~ ! [X130: $i] :
( ~ ( rel_s4 @ X6 @ X130 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X130 ) )
| ~ ! [X126: $i] :
( ~ ( rel_s4 @ X6 @ X126 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X126 ) )
| ~ ! [X122: $i] :
( ~ ( rel_s4 @ X6 @ X122 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X122 ) )
| ~ ! [X118: $i] :
( ~ ( rel_s4 @ X6 @ X118 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X118 ) )
| ~ ! [X114: $i] :
( ~ ( rel_s4 @ X6 @ X114 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X114 ) )
| ~ ! [X110: $i] :
( ~ ( rel_s4 @ X6 @ X110 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X110 ) ) )
| ~ ! [X8: $i] :
( ~ ( rel_s4 @ X6 @ X8 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X8 ) )
| ~ ! [X12: $i] :
( ~ ( rel_s4 @ X6 @ X12 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X12 ) )
| ~ ! [X16: $i] :
( ~ ( rel_s4 @ X6 @ X16 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X16 ) )
| ~ ! [X20: $i] :
( ~ ( rel_s4 @ X6 @ X20 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X20 ) )
| ~ ! [X24: $i] :
( ~ ( rel_s4 @ X6 @ X24 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X24 ) )
| ~ ! [X28: $i] :
( ~ ( rel_s4 @ X6 @ X28 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X28 ) )
| ~ ! [X32: $i] :
( ~ ( rel_s4 @ X6 @ X32 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X32 ) )
| ~ ! [X36: $i] :
( ~ ( rel_s4 @ X6 @ X36 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X36 ) )
| ~ ! [X40: $i] :
( ~ ( rel_s4 @ X6 @ X40 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X40 ) )
| ~ ! [X44: $i] :
( ~ ( rel_s4 @ X6 @ X44 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X44 ) )
| ~ ! [X48: $i] :
( ~ ( rel_s4 @ X6 @ X48 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X48 ) )
| ~ ! [X52: $i] :
( ~ ( rel_s4 @ X6 @ X52 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X52 ) )
| ~ ! [X56: $i] :
( ~ ( rel_s4 @ X6 @ X56 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X56 ) )
| ~ ! [X60: $i] :
( ~ ( rel_s4 @ X6 @ X60 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X60 ) )
| ~ ! [X64: $i] :
( ~ ( rel_s4 @ X6 @ X64 )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X64 ) )
| ~ ! [X88: $i] :
( ~ ( rel_s4 @ X6 @ X88 )
| ! [X90: mu] :
( ( exists_in_world @ X90 @ X88 )
=> ! [X92: $i] :
( ~ ( rel_s4 @ X88 @ X92 )
| ! [X94: mu] :
( ( exists_in_world @ X94 @ X92 )
=> ! [X96: $i] :
( ~ ( rel_s4 @ X92 @ X96 )
| ~ ( ~ ! [X108: $i] :
( ~ ( rel_s4 @ X96 @ X108 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X90 @ X94 ) @ use @ X108 ) )
| ~ ! [X106: $i] :
( ~ ( rel_s4 @ X96 @ X106 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X90 @ X94 ) @ use @ X106 ) ) )
| ~ ! [X98: $i] :
( ~ ( rel_s4 @ X96 @ X98 )
| ( leq @ n0 @ X90 @ X98 ) )
| ~ ! [X102: $i] :
( ~ ( rel_s4 @ X96 @ X102 )
| ( leq @ X90 @ n2 @ X102 ) )
| ~ ! [X104: $i] :
( ~ ( rel_s4 @ X96 @ X104 )
| ( leq @ X94 @ ( minus @ pv5 @ n1 ) @ X104 ) )
| ~ ! [X100: $i] :
( ~ ( rel_s4 @ X96 @ X100 )
| ( leq @ n0 @ X94 @ X100 ) ) ) ) ) ) )
| ~ ! [X66: $i] :
( ~ ( rel_s4 @ X6 @ X66 )
| ! [X68: mu] :
( ( exists_in_world @ X68 @ X66 )
=> ! [X70: $i] :
( ~ ( rel_s4 @ X66 @ X70 )
| ! [X72: mu] :
( ( exists_in_world @ X72 @ X70 )
=> ! [X74: $i] :
( ~ ( rel_s4 @ X70 @ X74 )
| ~ ( ~ ! [X86: $i] :
( ~ ( rel_s4 @ X74 @ X86 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X68 @ X72 ) @ use @ X86 ) )
| ~ ! [X84: $i] :
( ~ ( rel_s4 @ X74 @ X84 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X68 @ X72 ) @ use @ X84 ) ) )
| ~ ! [X76: $i] :
( ~ ( rel_s4 @ X74 @ X76 )
| ( leq @ n0 @ X68 @ X76 ) )
| ~ ! [X80: $i] :
( ~ ( rel_s4 @ X74 @ X80 )
| ( leq @ X68 @ n2 @ X80 ) )
| ~ ! [X82: $i] :
( ~ ( rel_s4 @ X74 @ X82 )
| ( leq @ X72 @ pv5 @ X82 ) )
| ~ ! [X78: $i] :
( ~ ( rel_s4 @ X74 @ X78 )
| ( leq @ n0 @ X72 @ X78 ) ) ) ) ) ) )
| ~ ! [X62: $i] :
( ~ ( rel_s4 @ X6 @ X62 )
| ( leq @ n0 @ pv5 @ X62 ) )
| ~ ! [X58: $i] :
( ~ ( rel_s4 @ X6 @ X58 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X58 ) )
| ~ ! [X54: $i] :
( ~ ( rel_s4 @ X6 @ X54 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X54 ) )
| ~ ! [X50: $i] :
( ~ ( rel_s4 @ X6 @ X50 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X50 ) )
| ~ ! [X46: $i] :
( ~ ( rel_s4 @ X6 @ X46 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X46 ) )
| ~ ! [X42: $i] :
( ~ ( rel_s4 @ X6 @ X42 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X42 ) )
| ~ ! [X38: $i] :
( ~ ( rel_s4 @ X6 @ X38 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X38 ) )
| ~ ! [X34: $i] :
( ~ ( rel_s4 @ X6 @ X34 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X34 ) )
| ~ ! [X30: $i] :
( ~ ( rel_s4 @ X6 @ X30 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X30 ) )
| ~ ! [X26: $i] :
( ~ ( rel_s4 @ X6 @ X26 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X26 ) )
| ~ ! [X22: $i] :
( ~ ( rel_s4 @ X6 @ X22 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X22 ) )
| ~ ! [X18: $i] :
( ~ ( rel_s4 @ X6 @ X18 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X18 ) )
| ~ ! [X14: $i] :
( ~ ( rel_s4 @ X6 @ X14 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X14 ) )
| ~ ! [X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X10 ) ) ),
inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl0,plain,
~ ( !!
@ ^ [Y0: $i] :
( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y6 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y3 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y3 @ n2 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y5 @ pv5 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y6 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y3 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y3 @ n2 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y5 @ ( minus @ pv5 @ n1 ) @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y6 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y3 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y3 @ n2 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y5 @ ( minus @ pv5 @ n1 ) @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( !!
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y6 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y3 @ Y5 ) @ use @ Y7 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y3 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y3 @ n2 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ Y5 @ pv5 @ Y7 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y7: $i] :
( ( (~) @ ( rel_s4 @ Y6 @ Y7 ) )
| ( leq @ n0 @ Y5 @ Y7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y2 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_1]) ).
thf(zip_derived_cl1,plain,
~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk1' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y2 @ n2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y4 @ pv5 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y2 @ n2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y4 @ ( minus @ pv5 @ n1 ) @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y2 @ n2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y4 @ ( minus @ pv5 @ n1 ) @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( !!
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y5 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y2 @ Y4 ) @ use @ Y6 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y2 @ n2 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ Y4 @ pv5 @ Y6 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y6: $i] :
( ( (~) @ ( rel_s4 @ Y5 @ Y6 ) )
| ( leq @ n0 @ Y4 @ Y6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y1 ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
~ ( ( (~) @ ( rel_s4 @ '#sk1' @ '#sk2' ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y0 ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl4,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl36,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl68,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk3' ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl100,plain,
( ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl104,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl100]) ).
thf(zip_derived_cl108,plain,
( ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl108_001,plain,
( ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl115,plain,
( '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl117,plain,
( ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl108,zip_derived_cl115]) ).
thf(zip_derived_cl101,plain,
( ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl68]) ).
thf(zip_derived_cl105,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl110,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl124,plain,
( ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ '#form7' ),
inference(renaming,[status(thm)],[zip_derived_cl117,zip_derived_cl110]) ).
thf(zip_derived_cl124_002,plain,
( ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ '#form7' ),
inference(renaming,[status(thm)],[zip_derived_cl117,zip_derived_cl110]) ).
thf(zip_derived_cl133,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl135,plain,
( ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5' ),
inference(renaming,[status(thm)],[zip_derived_cl124,zip_derived_cl133]) ).
thf(zip_derived_cl105_003,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl101]) ).
thf(zip_derived_cl110_004,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl112,plain,
( ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl105,zip_derived_cl110]) ).
thf(zip_derived_cl115_005,plain,
( '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl119,plain,
( ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5' ),
inference(renaming,[status(thm)],[zip_derived_cl112,zip_derived_cl115]) ).
thf(zip_derived_cl128,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl142,plain,
( ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl135,zip_derived_cl128]) ).
thf(zip_derived_cl142_006,plain,
( ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl135,zip_derived_cl128]) ).
thf(zip_derived_cl151,plain,
( '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl153,plain,
( ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl142,zip_derived_cl151]) ).
thf(zip_derived_cl119_007,plain,
( ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5' ),
inference(renaming,[status(thm)],[zip_derived_cl112,zip_derived_cl115]) ).
thf(zip_derived_cl128_008,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl130,plain,
( ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7' ),
inference(renaming,[status(thm)],[zip_derived_cl119,zip_derived_cl128]) ).
thf(zip_derived_cl133_009,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl137,plain,
( ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl130,zip_derived_cl133]) ).
thf(zip_derived_cl146,plain,
( '#form13'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl160,plain,
( ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15' ),
inference(renaming,[status(thm)],[zip_derived_cl153,zip_derived_cl146]) ).
thf(zip_derived_cl160_010,plain,
( ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15' ),
inference(renaming,[status(thm)],[zip_derived_cl153,zip_derived_cl146]) ).
thf(zip_derived_cl172,plain,
( '#form21'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl174,plain,
( ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13' ),
inference(renaming,[status(thm)],[zip_derived_cl160,zip_derived_cl172]) ).
thf(zip_derived_cl137_011,plain,
( ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl130,zip_derived_cl133]) ).
thf(zip_derived_cl146_012,plain,
( '#form13'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl148,plain,
( ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl137,zip_derived_cl146]) ).
thf(zip_derived_cl151_013,plain,
( '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl155,plain,
( ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13' ),
inference(renaming,[status(thm)],[zip_derived_cl148,zip_derived_cl151]) ).
thf(zip_derived_cl164,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl184,plain,
( ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21' ),
inference(renaming,[status(thm)],[zip_derived_cl174,zip_derived_cl164]) ).
thf(zip_derived_cl184_014,plain,
( ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21' ),
inference(renaming,[status(thm)],[zip_derived_cl174,zip_derived_cl164]) ).
thf(zip_derived_cl196,plain,
( '#form27'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl198,plain,
( ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl184,zip_derived_cl196]) ).
thf(zip_derived_cl155_015,plain,
( ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13' ),
inference(renaming,[status(thm)],[zip_derived_cl148,zip_derived_cl151]) ).
thf(zip_derived_cl164_016,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl166,plain,
( ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15' ),
inference(renaming,[status(thm)],[zip_derived_cl155,zip_derived_cl164]) ).
thf(zip_derived_cl172_017,plain,
( '#form21'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl176,plain,
( ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl166,zip_derived_cl172]) ).
thf(zip_derived_cl188,plain,
( '#form23'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl208,plain,
( ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27' ),
inference(renaming,[status(thm)],[zip_derived_cl198,zip_derived_cl188]) ).
thf(zip_derived_cl208_018,plain,
( ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27' ),
inference(renaming,[status(thm)],[zip_derived_cl198,zip_derived_cl188]) ).
thf(zip_derived_cl219,plain,
( '#form33'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl221,plain,
( ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23' ),
inference(renaming,[status(thm)],[zip_derived_cl208,zip_derived_cl219]) ).
thf(zip_derived_cl176_019,plain,
( ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl166,zip_derived_cl172]) ).
thf(zip_derived_cl188_020,plain,
( '#form23'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl190,plain,
( ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21' ),
inference(renaming,[status(thm)],[zip_derived_cl176,zip_derived_cl188]) ).
thf(zip_derived_cl196_021,plain,
( '#form27'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl200,plain,
( ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23' ),
inference(renaming,[status(thm)],[zip_derived_cl190,zip_derived_cl196]) ).
thf(zip_derived_cl212,plain,
( '#form30'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl235,plain,
( ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33' ),
inference(renaming,[status(thm)],[zip_derived_cl221,zip_derived_cl212]) ).
thf(zip_derived_cl235_022,plain,
( ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33' ),
inference(renaming,[status(thm)],[zip_derived_cl221,zip_derived_cl212]) ).
thf(zip_derived_cl248,plain,
( '#form38'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl250,plain,
( ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30' ),
inference(renaming,[status(thm)],[zip_derived_cl235,zip_derived_cl248]) ).
thf(zip_derived_cl200_023,plain,
( ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23' ),
inference(renaming,[status(thm)],[zip_derived_cl190,zip_derived_cl196]) ).
thf(zip_derived_cl212_024,plain,
( '#form30'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl214,plain,
( ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27' ),
inference(renaming,[status(thm)],[zip_derived_cl200,zip_derived_cl212]) ).
thf(zip_derived_cl219_025,plain,
( '#form33'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl223,plain,
( ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30' ),
inference(renaming,[status(thm)],[zip_derived_cl214,zip_derived_cl219]) ).
thf(zip_derived_cl239,plain,
( '#form36'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl261,plain,
( ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38' ),
inference(renaming,[status(thm)],[zip_derived_cl250,zip_derived_cl239]) ).
thf(zip_derived_cl261_026,plain,
( ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38' ),
inference(renaming,[status(thm)],[zip_derived_cl250,zip_derived_cl239]) ).
thf(zip_derived_cl268,plain,
( '#form42'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl270,plain,
( ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36' ),
inference(renaming,[status(thm)],[zip_derived_cl261,zip_derived_cl268]) ).
thf(zip_derived_cl223_027,plain,
( ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30' ),
inference(renaming,[status(thm)],[zip_derived_cl214,zip_derived_cl219]) ).
thf(zip_derived_cl239_028,plain,
( '#form36'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl241,plain,
( ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33' ),
inference(renaming,[status(thm)],[zip_derived_cl223,zip_derived_cl239]) ).
thf(zip_derived_cl248_029,plain,
( '#form38'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl252,plain,
( ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36' ),
inference(renaming,[status(thm)],[zip_derived_cl241,zip_derived_cl248]) ).
thf(zip_derived_cl265,plain,
( '#form40'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl275,plain,
( ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42' ),
inference(renaming,[status(thm)],[zip_derived_cl270,zip_derived_cl265]) ).
thf(zip_derived_cl275_030,plain,
( ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42' ),
inference(renaming,[status(thm)],[zip_derived_cl270,zip_derived_cl265]) ).
thf(zip_derived_cl282,plain,
( '#form46'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl284,plain,
( ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40' ),
inference(renaming,[status(thm)],[zip_derived_cl275,zip_derived_cl282]) ).
thf(zip_derived_cl252_031,plain,
( ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36' ),
inference(renaming,[status(thm)],[zip_derived_cl241,zip_derived_cl248]) ).
thf(zip_derived_cl265_032,plain,
( '#form40'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl267,plain,
( ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38' ),
inference(renaming,[status(thm)],[zip_derived_cl252,zip_derived_cl265]) ).
thf(zip_derived_cl268_033,plain,
( '#form42'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl272,plain,
( ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40' ),
inference(renaming,[status(thm)],[zip_derived_cl267,zip_derived_cl268]) ).
thf(zip_derived_cl279,plain,
( '#form44'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl289,plain,
( ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46' ),
inference(renaming,[status(thm)],[zip_derived_cl284,zip_derived_cl279]) ).
thf(zip_derived_cl289_034,plain,
( ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46' ),
inference(renaming,[status(thm)],[zip_derived_cl284,zip_derived_cl279]) ).
thf(zip_derived_cl296,plain,
( '#form50'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl298,plain,
( ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44' ),
inference(renaming,[status(thm)],[zip_derived_cl289,zip_derived_cl296]) ).
thf(zip_derived_cl272_035,plain,
( ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40' ),
inference(renaming,[status(thm)],[zip_derived_cl267,zip_derived_cl268]) ).
thf(zip_derived_cl279_036,plain,
( '#form44'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl281,plain,
( ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42' ),
inference(renaming,[status(thm)],[zip_derived_cl272,zip_derived_cl279]) ).
thf(zip_derived_cl282_037,plain,
( '#form46'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl286,plain,
( ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44' ),
inference(renaming,[status(thm)],[zip_derived_cl281,zip_derived_cl282]) ).
thf(zip_derived_cl293,plain,
( '#form48'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl303,plain,
( ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50' ),
inference(renaming,[status(thm)],[zip_derived_cl298,zip_derived_cl293]) ).
thf(zip_derived_cl303_038,plain,
( ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50' ),
inference(renaming,[status(thm)],[zip_derived_cl298,zip_derived_cl293]) ).
thf(zip_derived_cl310,plain,
( '#form54'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl312,plain,
( ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48' ),
inference(renaming,[status(thm)],[zip_derived_cl303,zip_derived_cl310]) ).
thf(zip_derived_cl286_039,plain,
( ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44' ),
inference(renaming,[status(thm)],[zip_derived_cl281,zip_derived_cl282]) ).
thf(zip_derived_cl293_040,plain,
( '#form48'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl295,plain,
( ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46' ),
inference(renaming,[status(thm)],[zip_derived_cl286,zip_derived_cl293]) ).
thf(zip_derived_cl296_041,plain,
( '#form50'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl300,plain,
( ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48' ),
inference(renaming,[status(thm)],[zip_derived_cl295,zip_derived_cl296]) ).
thf(zip_derived_cl307,plain,
( '#form52'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl317,plain,
( ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54' ),
inference(renaming,[status(thm)],[zip_derived_cl312,zip_derived_cl307]) ).
thf(zip_derived_cl21,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl53,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ pv5 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl85,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ pv5 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl103,plain,
! [X2: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ X4 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ X4 @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ pv5 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl85]) ).
thf(zip_derived_cl107,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ X4 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ X4 @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ pv5 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl103]) ).
thf(zip_derived_cl114,plain,
! [X2: $i,X4: mu,X6: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X6 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ X4 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ X4 @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl107]) ).
thf(zip_derived_cl123,plain,
! [X2: $i,X4: mu,X6: $i] :
( ~ ( rel_s4 @ X2 @ X6 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ X4 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ X4 @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl114]) ).
thf(zip_derived_cl132,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu] :
( ( ( exists_in_world @ X8 @ X6 )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X4 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X4 @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X8 @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X8 @ Y1 ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl123]) ).
thf(zip_derived_cl141,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu] :
( ~ ( exists_in_world @ X8 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X4 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X4 @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X8 @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X8 @ Y1 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl132]) ).
thf(zip_derived_cl150,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( (~) @ ( rel_s4 @ X6 @ X10 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl141]) ).
thf(zip_derived_cl159,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl169,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl324,plain,
( ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52' ),
inference(renaming,[status(thm)],[zip_derived_cl317,zip_derived_cl169]) ).
thf(zip_derived_cl300_042,plain,
( ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48' ),
inference(renaming,[status(thm)],[zip_derived_cl295,zip_derived_cl296]) ).
thf(zip_derived_cl307_043,plain,
( '#form52'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl309,plain,
( ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50' ),
inference(renaming,[status(thm)],[zip_derived_cl300,zip_derived_cl307]) ).
thf(zip_derived_cl310_044,plain,
( '#form54'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl314,plain,
( ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52' ),
inference(renaming,[status(thm)],[zip_derived_cl309,zip_derived_cl310]) ).
thf(zip_derived_cl321,plain,
( '#form56'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl329,plain,
( ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl324,zip_derived_cl321]) ).
thf(zip_derived_cl329_045,plain,
( ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl324,zip_derived_cl321]) ).
thf(zip_derived_cl334,plain,
( '#form60'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl336,plain,
( ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56' ),
inference(renaming,[status(thm)],[zip_derived_cl329,zip_derived_cl334]) ).
thf(zip_derived_cl314_046,plain,
( ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52' ),
inference(renaming,[status(thm)],[zip_derived_cl309,zip_derived_cl310]) ).
thf(zip_derived_cl321_047,plain,
( '#form56'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl323,plain,
( ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54' ),
inference(renaming,[status(thm)],[zip_derived_cl314,zip_derived_cl321]) ).
thf(zip_derived_cl169_048,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl326,plain,
( ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56' ),
inference(renaming,[status(thm)],[zip_derived_cl323,zip_derived_cl169]) ).
thf(zip_derived_cl331,plain,
( '#form58'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl341,plain,
( ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60' ),
inference(renaming,[status(thm)],[zip_derived_cl336,zip_derived_cl331]) ).
thf(zip_derived_cl348,plain,
( '#form64'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl349,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk65' ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk65' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk65' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ ( minus @ pv5 @ n1 ) @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl348]) ).
thf(zip_derived_cl358,plain,
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk65' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk65' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ ( minus @ pv5 @ n1 ) @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl349]) ).
thf(zip_derived_cl366,plain,
( ~ ( ( exists_in_world @ '#sk69' @ '#sk65' )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk65' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ '#sk69' @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ '#sk69' @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ ( minus @ pv5 @ n1 ) @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl358]) ).
thf(zip_derived_cl374,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk65' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ '#sk69' @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ '#sk69' @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ ( minus @ pv5 @ n1 ) @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl366]) ).
thf(zip_derived_cl377,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk65' @ '#sk71' ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk71' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk71' @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ '#sk69' @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ '#sk69' @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ ( minus @ pv5 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl374]) ).
thf(zip_derived_cl380,plain,
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk71' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk71' @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ '#sk69' @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ '#sk69' @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ ( minus @ pv5 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl377]) ).
thf(zip_derived_cl383,plain,
( ~ ( ( exists_in_world @ '#sk73' @ '#sk71' )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk71' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk69' @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk69' @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk73' @ Y1 ) ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl380]) ).
thf(zip_derived_cl386,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk71' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk69' @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk69' @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk73' @ Y1 ) ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl383]) ).
thf(zip_derived_cl393,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk71' @ '#sk75' ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ n0 @ '#sk69' @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ '#sk69' @ n2 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ n0 @ '#sk73' @ Y0 ) ) ) ) )
| '#form64' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl386]) ).
thf(zip_derived_cl399,plain,
( ( rel_s4 @ '#sk71' @ '#sk75' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl35,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl67,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl99,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl34,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl66,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl98,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl326_049,plain,
( ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56' ),
inference(renaming,[status(thm)],[zip_derived_cl323,zip_derived_cl169]) ).
thf(zip_derived_cl331_050,plain,
( '#form58'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl333,plain,
( ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl326,zip_derived_cl331]) ).
thf(zip_derived_cl334_051,plain,
( '#form60'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl338,plain,
( ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58' ),
inference(renaming,[status(thm)],[zip_derived_cl333,zip_derived_cl334]) ).
thf(zip_derived_cl338_052,plain,
( ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58' ),
inference(renaming,[status(thm)],[zip_derived_cl333,zip_derived_cl334]) ).
thf(zip_derived_cl345,plain,
( '#form62'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl347,plain,
( ~ '#form62'
| ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60' ),
inference(renaming,[status(thm)],[zip_derived_cl338,zip_derived_cl345]) ).
thf(zip_derived_cl348_053,plain,
( '#form64'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl353,plain,
( ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62' ),
inference(renaming,[status(thm)],[zip_derived_cl347,zip_derived_cl348]) ).
thf(zip_derived_cl353_054,plain,
( ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62' ),
inference(renaming,[status(thm)],[zip_derived_cl347,zip_derived_cl348]) ).
thf(zip_derived_cl362,plain,
( '#form67'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl364,plain,
( ~ '#form67'
| ~ '#form62'
| ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk4' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60'
| ~ '#form64' ),
inference(renaming,[status(thm)],[zip_derived_cl353,zip_derived_cl362]) ).
thf(zip_derived_cl370,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62'
| ~ '#form67' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl364]) ).
thf(zip_derived_cl22,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl54,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( leq @ n0 @ pv5 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl86,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( leq @ n0 @ pv5 @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl169_055,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl170,plain,
! [X4: mu,X10: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) ) )
| ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl169]) ).
thf(zip_derived_cl183,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl451,plain,
! [X0: $i] :
( ~ ( rel_s4 @ '#sk2' @ ( '#sk20' @ pv5 @ X0 ) )
| ( '#form19' @ pv5 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl86,zip_derived_cl183]) ).
thf(zip_derived_cl182,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl477,plain,
( ( '#form19' @ pv5 @ '#sk2' )
| ( '#form19' @ pv5 @ '#sk2' ) ),
inference('sup+',[status(thm)],[zip_derived_cl451,zip_derived_cl182]) ).
thf(zip_derived_cl482,plain,
'#form19' @ pv5 @ '#sk2',
inference(simplify,[status(thm)],[zip_derived_cl477]) ).
thf(zip_derived_cl23,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl55,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl87,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl310_056,plain,
( '#form54'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl311,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk55' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ '#sk55' ) )
| '#form54' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl310]) ).
thf(zip_derived_cl319,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ '#sk55' )
| '#form54' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl311]) ).
thf(zip_derived_cl555,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk55' )
| '#form54' ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl319]) ).
thf(zip_derived_cl318,plain,
( ( rel_s4 @ '#sk2' @ '#sk55' )
| '#form54' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl311]) ).
thf(zip_derived_cl559,plain,
'#form54',
inference(clc,[status(thm)],[zip_derived_cl555,zip_derived_cl318]) ).
thf(zip_derived_cl24,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl56,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl88,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl56]) ).
thf(zip_derived_cl296_057,plain,
( '#form50'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl297,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk51' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ '#sk51' ) )
| '#form50' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl296]) ).
thf(zip_derived_cl305,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ '#sk51' )
| '#form50' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl297]) ).
thf(zip_derived_cl560,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk51' )
| '#form50' ),
inference('sup-',[status(thm)],[zip_derived_cl88,zip_derived_cl305]) ).
thf(zip_derived_cl304,plain,
( ( rel_s4 @ '#sk2' @ '#sk51' )
| '#form50' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl297]) ).
thf(zip_derived_cl564,plain,
'#form50',
inference(clc,[status(thm)],[zip_derived_cl560,zip_derived_cl304]) ).
thf(zip_derived_cl25,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl57,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl89,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl282_058,plain,
( '#form46'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl283,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk47' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ '#sk47' ) )
| '#form46' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl282]) ).
thf(zip_derived_cl291,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ '#sk47' )
| '#form46' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl283]) ).
thf(zip_derived_cl565,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk47' )
| '#form46' ),
inference('sup-',[status(thm)],[zip_derived_cl89,zip_derived_cl291]) ).
thf(zip_derived_cl290,plain,
( ( rel_s4 @ '#sk2' @ '#sk47' )
| '#form46' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl283]) ).
thf(zip_derived_cl577,plain,
'#form46',
inference(clc,[status(thm)],[zip_derived_cl565,zip_derived_cl290]) ).
thf(zip_derived_cl26,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl58,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl90,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl268_059,plain,
( '#form42'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl269,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk43' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ '#sk43' ) )
| '#form42' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl268]) ).
thf(zip_derived_cl277,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ '#sk43' )
| '#form42' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl269]) ).
thf(zip_derived_cl578,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk43' )
| '#form42' ),
inference('sup-',[status(thm)],[zip_derived_cl90,zip_derived_cl277]) ).
thf(zip_derived_cl276,plain,
( ( rel_s4 @ '#sk2' @ '#sk43' )
| '#form42' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl269]) ).
thf(zip_derived_cl582,plain,
'#form42',
inference(clc,[status(thm)],[zip_derived_cl578,zip_derived_cl276]) ).
thf(zip_derived_cl27,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl59,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl91,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl248_060,plain,
( '#form38'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl249,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk39' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ '#sk39' ) )
| '#form38' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl248]) ).
thf(zip_derived_cl263,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ '#sk39' )
| '#form38' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl249]) ).
thf(zip_derived_cl583,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk39' )
| '#form38' ),
inference('sup-',[status(thm)],[zip_derived_cl91,zip_derived_cl263]) ).
thf(zip_derived_cl262,plain,
( ( rel_s4 @ '#sk2' @ '#sk39' )
| '#form38' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl249]) ).
thf(zip_derived_cl587,plain,
'#form38',
inference(clc,[status(thm)],[zip_derived_cl583,zip_derived_cl262]) ).
thf(zip_derived_cl28,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl60,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl92,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl60]) ).
thf(zip_derived_cl219_061,plain,
( '#form33'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl220,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk34' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ '#sk34' ) )
| '#form33' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl219]) ).
thf(zip_derived_cl237,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ '#sk34' )
| '#form33' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl588,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk34' )
| '#form33' ),
inference('sup-',[status(thm)],[zip_derived_cl92,zip_derived_cl237]) ).
thf(zip_derived_cl236,plain,
( ( rel_s4 @ '#sk2' @ '#sk34' )
| '#form33' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl220]) ).
thf(zip_derived_cl592,plain,
'#form33',
inference(clc,[status(thm)],[zip_derived_cl588,zip_derived_cl236]) ).
thf(zip_derived_cl29,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl61,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl93,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl196_062,plain,
( '#form27'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl197,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk28' ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ '#sk28' ) )
| '#form27' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl196]) ).
thf(zip_derived_cl210,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ '#sk28' )
| '#form27' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl593,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk28' )
| '#form27' ),
inference('sup-',[status(thm)],[zip_derived_cl93,zip_derived_cl210]) ).
thf(zip_derived_cl209,plain,
( ( rel_s4 @ '#sk2' @ '#sk28' )
| '#form27' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl197]) ).
thf(zip_derived_cl597,plain,
'#form27',
inference(clc,[status(thm)],[zip_derived_cl593,zip_derived_cl209]) ).
thf(zip_derived_cl30,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl62,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl94,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl172_063,plain,
( '#form21'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl173,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk22' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ '#sk22' ) )
| '#form21' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl172]) ).
thf(zip_derived_cl186,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ '#sk22' )
| '#form21' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl620,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk22' )
| '#form21' ),
inference('sup-',[status(thm)],[zip_derived_cl94,zip_derived_cl186]) ).
thf(zip_derived_cl185,plain,
( ( rel_s4 @ '#sk2' @ '#sk22' )
| '#form21' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl173]) ).
thf(zip_derived_cl624,plain,
'#form21',
inference(clc,[status(thm)],[zip_derived_cl620,zip_derived_cl185]) ).
thf(zip_derived_cl31,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl63,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl95,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl151_064,plain,
( '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl152,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk16' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ '#sk16' ) )
| '#form15' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl151]) ).
thf(zip_derived_cl162,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ '#sk16' )
| '#form15' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl625,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk16' )
| '#form15' ),
inference('sup-',[status(thm)],[zip_derived_cl95,zip_derived_cl162]) ).
thf(zip_derived_cl161,plain,
( ( rel_s4 @ '#sk2' @ '#sk16' )
| '#form15' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl152]) ).
thf(zip_derived_cl629,plain,
'#form15',
inference(clc,[status(thm)],[zip_derived_cl625,zip_derived_cl161]) ).
thf(zip_derived_cl32,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl64,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl96,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl64]) ).
thf(zip_derived_cl133_065,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl134,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk12' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ '#sk12' ) )
| '#form11' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl133]) ).
thf(zip_derived_cl144,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ '#sk12' )
| '#form11' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl598,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk12' )
| '#form11' ),
inference('sup-',[status(thm)],[zip_derived_cl96,zip_derived_cl144]) ).
thf(zip_derived_cl143,plain,
( ( rel_s4 @ '#sk2' @ '#sk12' )
| '#form11' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl134]) ).
thf(zip_derived_cl602,plain,
'#form11',
inference(clc,[status(thm)],[zip_derived_cl598,zip_derived_cl143]) ).
thf(zip_derived_cl33,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl65,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl97,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl65]) ).
thf(zip_derived_cl115_066,plain,
( '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl116,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk8' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ '#sk8' ) )
| '#form7' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl115]) ).
thf(zip_derived_cl126,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ '#sk8' )
| '#form7' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl615,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk8' )
| '#form7' ),
inference('sup-',[status(thm)],[zip_derived_cl97,zip_derived_cl126]) ).
thf(zip_derived_cl125,plain,
( ( rel_s4 @ '#sk2' @ '#sk8' )
| '#form7' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl116]) ).
thf(zip_derived_cl619,plain,
'#form7',
inference(clc,[status(thm)],[zip_derived_cl615,zip_derived_cl125]) ).
thf(zip_derived_cl5,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl37,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl69,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl110_067,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl111,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk6' ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ '#sk6' ) )
| '#form5' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl110]) ).
thf(zip_derived_cl121,plain,
( ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ '#sk6' )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl436,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk6' )
| '#form5' ),
inference('sup-',[status(thm)],[zip_derived_cl69,zip_derived_cl121]) ).
thf(zip_derived_cl120,plain,
( ( rel_s4 @ '#sk2' @ '#sk6' )
| '#form5' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl111]) ).
thf(zip_derived_cl440,plain,
'#form5',
inference(clc,[status(thm)],[zip_derived_cl436,zip_derived_cl120]) ).
thf(zip_derived_cl6,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl38,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl70,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl128_068,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl129,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk10' ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ '#sk10' ) )
| '#form9' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl128]) ).
thf(zip_derived_cl139,plain,
( ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ '#sk10' )
| '#form9' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl441,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk10' )
| '#form9' ),
inference('sup-',[status(thm)],[zip_derived_cl70,zip_derived_cl139]) ).
thf(zip_derived_cl138,plain,
( ( rel_s4 @ '#sk2' @ '#sk10' )
| '#form9' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl129]) ).
thf(zip_derived_cl445,plain,
'#form9',
inference(clc,[status(thm)],[zip_derived_cl441,zip_derived_cl138]) ).
thf(zip_derived_cl7,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl39,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl71,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl146_069,plain,
( '#form13'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl147,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk14' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ '#sk14' ) )
| '#form13' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl146]) ).
thf(zip_derived_cl157,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ '#sk14' )
| '#form13' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl446,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk14' )
| '#form13' ),
inference('sup-',[status(thm)],[zip_derived_cl71,zip_derived_cl157]) ).
thf(zip_derived_cl156,plain,
( ( rel_s4 @ '#sk2' @ '#sk14' )
| '#form13' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl147]) ).
thf(zip_derived_cl450,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl446,zip_derived_cl156]) ).
thf(zip_derived_cl8,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl40,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl72,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl164_070,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl165,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk18' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ '#sk18' ) )
| '#form17' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl164]) ).
thf(zip_derived_cl178,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ '#sk18' )
| '#form17' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl455,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk18' )
| '#form17' ),
inference('sup-',[status(thm)],[zip_derived_cl72,zip_derived_cl178]) ).
thf(zip_derived_cl177,plain,
( ( rel_s4 @ '#sk2' @ '#sk18' )
| '#form17' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl165]) ).
thf(zip_derived_cl459,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl455,zip_derived_cl177]) ).
thf(zip_derived_cl9,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl41,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl73,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl188_071,plain,
( '#form23'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl189,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk24' ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ '#sk24' ) )
| '#form23' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl188]) ).
thf(zip_derived_cl202,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ '#sk24' )
| '#form23' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl460,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk24' )
| '#form23' ),
inference('sup-',[status(thm)],[zip_derived_cl73,zip_derived_cl202]) ).
thf(zip_derived_cl201,plain,
( ( rel_s4 @ '#sk2' @ '#sk24' )
| '#form23' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl189]) ).
thf(zip_derived_cl464,plain,
'#form23',
inference(clc,[status(thm)],[zip_derived_cl460,zip_derived_cl201]) ).
thf(zip_derived_cl10,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl42,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl74,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl212_072,plain,
( '#form30'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl213,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk31' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ '#sk31' ) )
| '#form30' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl212]) ).
thf(zip_derived_cl225,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ '#sk31' )
| '#form30' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl213]) ).
thf(zip_derived_cl470,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk31' )
| '#form30' ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl225]) ).
thf(zip_derived_cl224,plain,
( ( rel_s4 @ '#sk2' @ '#sk31' )
| '#form30' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl213]) ).
thf(zip_derived_cl498,plain,
'#form30',
inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl224]) ).
thf(zip_derived_cl11,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl43,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl75,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl239_073,plain,
( '#form36'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl240,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk37' ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ '#sk37' ) )
| '#form36' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl239]) ).
thf(zip_derived_cl254,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ '#sk37' )
| '#form36' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl240]) ).
thf(zip_derived_cl465,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk37' )
| '#form36' ),
inference('sup-',[status(thm)],[zip_derived_cl75,zip_derived_cl254]) ).
thf(zip_derived_cl253,plain,
( ( rel_s4 @ '#sk2' @ '#sk37' )
| '#form36' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl240]) ).
thf(zip_derived_cl469,plain,
'#form36',
inference(clc,[status(thm)],[zip_derived_cl465,zip_derived_cl253]) ).
thf(zip_derived_cl12,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl44,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl76,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl44]) ).
thf(zip_derived_cl265_074,plain,
( '#form40'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl266,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk41' ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ '#sk41' ) )
| '#form40' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl265]) ).
thf(zip_derived_cl274,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ '#sk41' )
| '#form40' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl266]) ).
thf(zip_derived_cl515,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk41' )
| '#form40' ),
inference('sup-',[status(thm)],[zip_derived_cl76,zip_derived_cl274]) ).
thf(zip_derived_cl273,plain,
( ( rel_s4 @ '#sk2' @ '#sk41' )
| '#form40' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl266]) ).
thf(zip_derived_cl519,plain,
'#form40',
inference(clc,[status(thm)],[zip_derived_cl515,zip_derived_cl273]) ).
thf(zip_derived_cl13,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl45,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl77,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl279_075,plain,
( '#form44'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl280,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk45' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ '#sk45' ) )
| '#form44' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl279]) ).
thf(zip_derived_cl288,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ '#sk45' )
| '#form44' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl280]) ).
thf(zip_derived_cl520,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk45' )
| '#form44' ),
inference('sup-',[status(thm)],[zip_derived_cl77,zip_derived_cl288]) ).
thf(zip_derived_cl287,plain,
( ( rel_s4 @ '#sk2' @ '#sk45' )
| '#form44' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl280]) ).
thf(zip_derived_cl524,plain,
'#form44',
inference(clc,[status(thm)],[zip_derived_cl520,zip_derived_cl287]) ).
thf(zip_derived_cl14,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl46,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl78,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl293_076,plain,
( '#form48'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl294,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk49' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ '#sk49' ) )
| '#form48' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl293]) ).
thf(zip_derived_cl302,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ '#sk49' )
| '#form48' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl294]) ).
thf(zip_derived_cl525,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk49' )
| '#form48' ),
inference('sup-',[status(thm)],[zip_derived_cl78,zip_derived_cl302]) ).
thf(zip_derived_cl301,plain,
( ( rel_s4 @ '#sk2' @ '#sk49' )
| '#form48' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl294]) ).
thf(zip_derived_cl529,plain,
'#form48',
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl301]) ).
thf(zip_derived_cl15,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl47,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl79,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl307_077,plain,
( '#form52'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl308,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk53' ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ '#sk53' ) )
| '#form52' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl307]) ).
thf(zip_derived_cl316,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ '#sk53' )
| '#form52' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl308]) ).
thf(zip_derived_cl530,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk53' )
| '#form52' ),
inference('sup-',[status(thm)],[zip_derived_cl79,zip_derived_cl316]) ).
thf(zip_derived_cl315,plain,
( ( rel_s4 @ '#sk2' @ '#sk53' )
| '#form52' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl308]) ).
thf(zip_derived_cl534,plain,
'#form52',
inference(clc,[status(thm)],[zip_derived_cl530,zip_derived_cl315]) ).
thf(zip_derived_cl16,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl48,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl80,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl48]) ).
thf(zip_derived_cl321_078,plain,
( '#form56'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl322,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk57' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ '#sk57' ) )
| '#form56' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl321]) ).
thf(zip_derived_cl328,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ '#sk57' )
| '#form56' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl535,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk57' )
| '#form56' ),
inference('sup-',[status(thm)],[zip_derived_cl80,zip_derived_cl328]) ).
thf(zip_derived_cl327,plain,
( ( rel_s4 @ '#sk2' @ '#sk57' )
| '#form56' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl322]) ).
thf(zip_derived_cl539,plain,
'#form56',
inference(clc,[status(thm)],[zip_derived_cl535,zip_derived_cl327]) ).
thf(zip_derived_cl17,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl49,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl81,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl331_079,plain,
( '#form58'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl332,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk59' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ '#sk59' ) )
| '#form58' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl331]) ).
thf(zip_derived_cl340,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ '#sk59' )
| '#form58' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl332]) ).
thf(zip_derived_cl540,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk59' )
| '#form58' ),
inference('sup-',[status(thm)],[zip_derived_cl81,zip_derived_cl340]) ).
thf(zip_derived_cl339,plain,
( ( rel_s4 @ '#sk2' @ '#sk59' )
| '#form58' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl332]) ).
thf(zip_derived_cl544,plain,
'#form58',
inference(clc,[status(thm)],[zip_derived_cl540,zip_derived_cl339]) ).
thf(zip_derived_cl18,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl50,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl82,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl345_080,plain,
( '#form62'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl346,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk63' ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ '#sk63' ) )
| '#form62' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl345]) ).
thf(zip_derived_cl355,plain,
( ~ ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ '#sk63' )
| '#form62' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl346]) ).
thf(zip_derived_cl545,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk63' )
| '#form62' ),
inference('sup-',[status(thm)],[zip_derived_cl82,zip_derived_cl355]) ).
thf(zip_derived_cl354,plain,
( ( rel_s4 @ '#sk2' @ '#sk63' )
| '#form62' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl346]) ).
thf(zip_derived_cl549,plain,
'#form62',
inference(clc,[status(thm)],[zip_derived_cl545,zip_derived_cl354]) ).
thf(zip_derived_cl19,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl51,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl83,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl362_081,plain,
( '#form67'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl363,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk68' ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ '#sk68' ) )
| '#form67' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl362]) ).
thf(zip_derived_cl372,plain,
( ~ ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ '#sk68' )
| '#form67' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl363]) ).
thf(zip_derived_cl550,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk68' )
| '#form67' ),
inference('sup-',[status(thm)],[zip_derived_cl83,zip_derived_cl372]) ).
thf(zip_derived_cl371,plain,
( ( rel_s4 @ '#sk2' @ '#sk68' )
| '#form67' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl363]) ).
thf(zip_derived_cl554,plain,
'#form67',
inference(clc,[status(thm)],[zip_derived_cl550,zip_derived_cl371]) ).
thf(zip_derived_cl1105,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form64'
| ~ '#form60'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl370,zip_derived_cl482,zip_derived_cl559,zip_derived_cl564,zip_derived_cl577,zip_derived_cl582,zip_derived_cl587,zip_derived_cl592,zip_derived_cl597,zip_derived_cl624,zip_derived_cl629,zip_derived_cl602,zip_derived_cl619,zip_derived_cl440,zip_derived_cl445,zip_derived_cl450,zip_derived_cl459,zip_derived_cl464,zip_derived_cl498,zip_derived_cl469,zip_derived_cl519,zip_derived_cl524,zip_derived_cl529,zip_derived_cl534,zip_derived_cl539,zip_derived_cl544,zip_derived_cl549,zip_derived_cl554]) ).
thf(zip_derived_cl1106,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form60'
| ~ '#form64' ),
inference('sup-',[status(thm)],[zip_derived_cl98,zip_derived_cl1105]) ).
thf(zip_derived_cl369,plain,
( ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62'
| ~ '#form67' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl364]) ).
thf(zip_derived_cl482_082,plain,
'#form19' @ pv5 @ '#sk2',
inference(simplify,[status(thm)],[zip_derived_cl477]) ).
thf(zip_derived_cl559_083,plain,
'#form54',
inference(clc,[status(thm)],[zip_derived_cl555,zip_derived_cl318]) ).
thf(zip_derived_cl564_084,plain,
'#form50',
inference(clc,[status(thm)],[zip_derived_cl560,zip_derived_cl304]) ).
thf(zip_derived_cl577_085,plain,
'#form46',
inference(clc,[status(thm)],[zip_derived_cl565,zip_derived_cl290]) ).
thf(zip_derived_cl582_086,plain,
'#form42',
inference(clc,[status(thm)],[zip_derived_cl578,zip_derived_cl276]) ).
thf(zip_derived_cl587_087,plain,
'#form38',
inference(clc,[status(thm)],[zip_derived_cl583,zip_derived_cl262]) ).
thf(zip_derived_cl592_088,plain,
'#form33',
inference(clc,[status(thm)],[zip_derived_cl588,zip_derived_cl236]) ).
thf(zip_derived_cl597_089,plain,
'#form27',
inference(clc,[status(thm)],[zip_derived_cl593,zip_derived_cl209]) ).
thf(zip_derived_cl624_090,plain,
'#form21',
inference(clc,[status(thm)],[zip_derived_cl620,zip_derived_cl185]) ).
thf(zip_derived_cl629_091,plain,
'#form15',
inference(clc,[status(thm)],[zip_derived_cl625,zip_derived_cl161]) ).
thf(zip_derived_cl602_092,plain,
'#form11',
inference(clc,[status(thm)],[zip_derived_cl598,zip_derived_cl143]) ).
thf(zip_derived_cl619_093,plain,
'#form7',
inference(clc,[status(thm)],[zip_derived_cl615,zip_derived_cl125]) ).
thf(zip_derived_cl440_094,plain,
'#form5',
inference(clc,[status(thm)],[zip_derived_cl436,zip_derived_cl120]) ).
thf(zip_derived_cl445_095,plain,
'#form9',
inference(clc,[status(thm)],[zip_derived_cl441,zip_derived_cl138]) ).
thf(zip_derived_cl450_096,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl446,zip_derived_cl156]) ).
thf(zip_derived_cl459_097,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl455,zip_derived_cl177]) ).
thf(zip_derived_cl464_098,plain,
'#form23',
inference(clc,[status(thm)],[zip_derived_cl460,zip_derived_cl201]) ).
thf(zip_derived_cl498_099,plain,
'#form30',
inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl224]) ).
thf(zip_derived_cl469_100,plain,
'#form36',
inference(clc,[status(thm)],[zip_derived_cl465,zip_derived_cl253]) ).
thf(zip_derived_cl519_101,plain,
'#form40',
inference(clc,[status(thm)],[zip_derived_cl515,zip_derived_cl273]) ).
thf(zip_derived_cl524_102,plain,
'#form44',
inference(clc,[status(thm)],[zip_derived_cl520,zip_derived_cl287]) ).
thf(zip_derived_cl529_103,plain,
'#form48',
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl301]) ).
thf(zip_derived_cl534_104,plain,
'#form52',
inference(clc,[status(thm)],[zip_derived_cl530,zip_derived_cl315]) ).
thf(zip_derived_cl539_105,plain,
'#form56',
inference(clc,[status(thm)],[zip_derived_cl535,zip_derived_cl327]) ).
thf(zip_derived_cl544_106,plain,
'#form58',
inference(clc,[status(thm)],[zip_derived_cl540,zip_derived_cl339]) ).
thf(zip_derived_cl549_107,plain,
'#form62',
inference(clc,[status(thm)],[zip_derived_cl545,zip_derived_cl354]) ).
thf(zip_derived_cl554_108,plain,
'#form67',
inference(clc,[status(thm)],[zip_derived_cl550,zip_derived_cl371]) ).
thf(zip_derived_cl1084,plain,
( ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form64'
| ~ '#form60'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) ),
inference(demod,[status(thm)],[zip_derived_cl369,zip_derived_cl482,zip_derived_cl559,zip_derived_cl564,zip_derived_cl577,zip_derived_cl582,zip_derived_cl587,zip_derived_cl592,zip_derived_cl597,zip_derived_cl624,zip_derived_cl629,zip_derived_cl602,zip_derived_cl619,zip_derived_cl440,zip_derived_cl445,zip_derived_cl450,zip_derived_cl459,zip_derived_cl464,zip_derived_cl498,zip_derived_cl469,zip_derived_cl519,zip_derived_cl524,zip_derived_cl529,zip_derived_cl534,zip_derived_cl539,zip_derived_cl544,zip_derived_cl549,zip_derived_cl554]) ).
thf(zip_derived_cl99_109,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl1085,plain,
( ~ '#form60'
| ~ '#form64'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ ( rel_s4 @ '#sk2' @ '#sk3' ) ),
inference('sup+',[status(thm)],[zip_derived_cl1084,zip_derived_cl99]) ).
thf(zip_derived_cl109,plain,
( ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl104]) ).
thf(zip_derived_cl115_110,plain,
( '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl118,plain,
( ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) ),
inference(renaming,[status(thm)],[zip_derived_cl109,zip_derived_cl115]) ).
thf(zip_derived_cl110_111,plain,
( '#form5'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl127,plain,
( ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ '#form7' ),
inference(renaming,[status(thm)],[zip_derived_cl118,zip_derived_cl110]) ).
thf(zip_derived_cl133_112,plain,
( '#form11'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl136,plain,
( ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5' ),
inference(renaming,[status(thm)],[zip_derived_cl127,zip_derived_cl133]) ).
thf(zip_derived_cl128_113,plain,
( '#form9'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl145,plain,
( ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11' ),
inference(renaming,[status(thm)],[zip_derived_cl136,zip_derived_cl128]) ).
thf(zip_derived_cl151_114,plain,
( '#form15'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl154,plain,
( ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9' ),
inference(renaming,[status(thm)],[zip_derived_cl145,zip_derived_cl151]) ).
thf(zip_derived_cl146_115,plain,
( '#form13'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl163,plain,
( ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15' ),
inference(renaming,[status(thm)],[zip_derived_cl154,zip_derived_cl146]) ).
thf(zip_derived_cl172_116,plain,
( '#form21'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl175,plain,
( ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13' ),
inference(renaming,[status(thm)],[zip_derived_cl163,zip_derived_cl172]) ).
thf(zip_derived_cl164_117,plain,
( '#form17'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl187,plain,
( ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21' ),
inference(renaming,[status(thm)],[zip_derived_cl175,zip_derived_cl164]) ).
thf(zip_derived_cl196_118,plain,
( '#form27'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl199,plain,
( ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17' ),
inference(renaming,[status(thm)],[zip_derived_cl187,zip_derived_cl196]) ).
thf(zip_derived_cl188_119,plain,
( '#form23'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl211,plain,
( ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27' ),
inference(renaming,[status(thm)],[zip_derived_cl199,zip_derived_cl188]) ).
thf(zip_derived_cl219_120,plain,
( '#form33'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl222,plain,
( ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23' ),
inference(renaming,[status(thm)],[zip_derived_cl211,zip_derived_cl219]) ).
thf(zip_derived_cl212_121,plain,
( '#form30'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl238,plain,
( ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33' ),
inference(renaming,[status(thm)],[zip_derived_cl222,zip_derived_cl212]) ).
thf(zip_derived_cl248_122,plain,
( '#form38'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl251,plain,
( ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30' ),
inference(renaming,[status(thm)],[zip_derived_cl238,zip_derived_cl248]) ).
thf(zip_derived_cl239_123,plain,
( '#form36'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl264,plain,
( ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38' ),
inference(renaming,[status(thm)],[zip_derived_cl251,zip_derived_cl239]) ).
thf(zip_derived_cl268_124,plain,
( '#form42'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl271,plain,
( ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36' ),
inference(renaming,[status(thm)],[zip_derived_cl264,zip_derived_cl268]) ).
thf(zip_derived_cl265_125,plain,
( '#form40'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl278,plain,
( ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42' ),
inference(renaming,[status(thm)],[zip_derived_cl271,zip_derived_cl265]) ).
thf(zip_derived_cl282_126,plain,
( '#form46'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl285,plain,
( ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40' ),
inference(renaming,[status(thm)],[zip_derived_cl278,zip_derived_cl282]) ).
thf(zip_derived_cl279_127,plain,
( '#form44'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl292,plain,
( ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46' ),
inference(renaming,[status(thm)],[zip_derived_cl285,zip_derived_cl279]) ).
thf(zip_derived_cl296_128,plain,
( '#form50'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl299,plain,
( ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44' ),
inference(renaming,[status(thm)],[zip_derived_cl292,zip_derived_cl296]) ).
thf(zip_derived_cl293_129,plain,
( '#form48'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl306,plain,
( ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50' ),
inference(renaming,[status(thm)],[zip_derived_cl299,zip_derived_cl293]) ).
thf(zip_derived_cl310_130,plain,
( '#form54'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl313,plain,
( ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48' ),
inference(renaming,[status(thm)],[zip_derived_cl306,zip_derived_cl310]) ).
thf(zip_derived_cl307_131,plain,
( '#form52'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl320,plain,
( ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ n0 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54' ),
inference(renaming,[status(thm)],[zip_derived_cl313,zip_derived_cl307]) ).
thf(zip_derived_cl169_132,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl325,plain,
( ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52' ),
inference(renaming,[status(thm)],[zip_derived_cl320,zip_derived_cl169]) ).
thf(zip_derived_cl321_133,plain,
( '#form56'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl330,plain,
( ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' ) ),
inference(renaming,[status(thm)],[zip_derived_cl325,zip_derived_cl321]) ).
thf(zip_derived_cl334_134,plain,
( '#form60'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl337,plain,
( ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56' ),
inference(renaming,[status(thm)],[zip_derived_cl330,zip_derived_cl334]) ).
thf(zip_derived_cl331_135,plain,
( '#form58'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl344,plain,
( ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60' ),
inference(renaming,[status(thm)],[zip_derived_cl337,zip_derived_cl331]) ).
thf(zip_derived_cl348_136,plain,
( '#form64'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl352,plain,
( ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58' ),
inference(renaming,[status(thm)],[zip_derived_cl344,zip_derived_cl348]) ).
thf(zip_derived_cl345_137,plain,
( '#form62'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl361,plain,
( ~ '#form62'
| ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60'
| ~ '#form64' ),
inference(renaming,[status(thm)],[zip_derived_cl352,zip_derived_cl345]) ).
thf(zip_derived_cl362_138,plain,
( '#form67'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl368,plain,
( ~ '#form67'
| ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62' ),
inference(renaming,[status(thm)],[zip_derived_cl361,zip_derived_cl362]) ).
thf(zip_derived_cl554_139,plain,
'#form67',
inference(clc,[status(thm)],[zip_derived_cl550,zip_derived_cl371]) ).
thf(zip_derived_cl482_140,plain,
'#form19' @ pv5 @ '#sk2',
inference(simplify,[status(thm)],[zip_derived_cl477]) ).
thf(zip_derived_cl559_141,plain,
'#form54',
inference(clc,[status(thm)],[zip_derived_cl555,zip_derived_cl318]) ).
thf(zip_derived_cl564_142,plain,
'#form50',
inference(clc,[status(thm)],[zip_derived_cl560,zip_derived_cl304]) ).
thf(zip_derived_cl577_143,plain,
'#form46',
inference(clc,[status(thm)],[zip_derived_cl565,zip_derived_cl290]) ).
thf(zip_derived_cl582_144,plain,
'#form42',
inference(clc,[status(thm)],[zip_derived_cl578,zip_derived_cl276]) ).
thf(zip_derived_cl587_145,plain,
'#form38',
inference(clc,[status(thm)],[zip_derived_cl583,zip_derived_cl262]) ).
thf(zip_derived_cl592_146,plain,
'#form33',
inference(clc,[status(thm)],[zip_derived_cl588,zip_derived_cl236]) ).
thf(zip_derived_cl597_147,plain,
'#form27',
inference(clc,[status(thm)],[zip_derived_cl593,zip_derived_cl209]) ).
thf(zip_derived_cl624_148,plain,
'#form21',
inference(clc,[status(thm)],[zip_derived_cl620,zip_derived_cl185]) ).
thf(zip_derived_cl629_149,plain,
'#form15',
inference(clc,[status(thm)],[zip_derived_cl625,zip_derived_cl161]) ).
thf(zip_derived_cl602_150,plain,
'#form11',
inference(clc,[status(thm)],[zip_derived_cl598,zip_derived_cl143]) ).
thf(zip_derived_cl619_151,plain,
'#form7',
inference(clc,[status(thm)],[zip_derived_cl615,zip_derived_cl125]) ).
thf(zip_derived_cl440_152,plain,
'#form5',
inference(clc,[status(thm)],[zip_derived_cl436,zip_derived_cl120]) ).
thf(zip_derived_cl445_153,plain,
'#form9',
inference(clc,[status(thm)],[zip_derived_cl441,zip_derived_cl138]) ).
thf(zip_derived_cl450_154,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl446,zip_derived_cl156]) ).
thf(zip_derived_cl459_155,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl455,zip_derived_cl177]) ).
thf(zip_derived_cl464_156,plain,
'#form23',
inference(clc,[status(thm)],[zip_derived_cl460,zip_derived_cl201]) ).
thf(zip_derived_cl498_157,plain,
'#form30',
inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl224]) ).
thf(zip_derived_cl469_158,plain,
'#form36',
inference(clc,[status(thm)],[zip_derived_cl465,zip_derived_cl253]) ).
thf(zip_derived_cl519_159,plain,
'#form40',
inference(clc,[status(thm)],[zip_derived_cl515,zip_derived_cl273]) ).
thf(zip_derived_cl524_160,plain,
'#form44',
inference(clc,[status(thm)],[zip_derived_cl520,zip_derived_cl287]) ).
thf(zip_derived_cl529_161,plain,
'#form48',
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl301]) ).
thf(zip_derived_cl534_162,plain,
'#form52',
inference(clc,[status(thm)],[zip_derived_cl530,zip_derived_cl315]) ).
thf(zip_derived_cl539_163,plain,
'#form56',
inference(clc,[status(thm)],[zip_derived_cl535,zip_derived_cl327]) ).
thf(zip_derived_cl544_164,plain,
'#form58',
inference(clc,[status(thm)],[zip_derived_cl540,zip_derived_cl339]) ).
thf(zip_derived_cl549_165,plain,
'#form62',
inference(clc,[status(thm)],[zip_derived_cl545,zip_derived_cl354]) ).
thf(zip_derived_cl1031,plain,
( ~ '#form64'
| ~ '#form60'
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl368,zip_derived_cl554,zip_derived_cl482,zip_derived_cl559,zip_derived_cl564,zip_derived_cl577,zip_derived_cl582,zip_derived_cl587,zip_derived_cl592,zip_derived_cl597,zip_derived_cl624,zip_derived_cl629,zip_derived_cl602,zip_derived_cl619,zip_derived_cl440,zip_derived_cl445,zip_derived_cl450,zip_derived_cl459,zip_derived_cl464,zip_derived_cl498,zip_derived_cl469,zip_derived_cl519,zip_derived_cl524,zip_derived_cl529,zip_derived_cl534,zip_derived_cl539,zip_derived_cl544,zip_derived_cl549]) ).
thf(zip_derived_cl98_166,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl1032,plain,
( ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ '#form60'
| ~ '#form64'
| ~ ( rel_s4 @ '#sk2' @ '#sk4' ) ),
inference('sup+',[status(thm)],[zip_derived_cl1031,zip_derived_cl98]) ).
thf(zip_derived_cl341_167,plain,
( ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60' ),
inference(renaming,[status(thm)],[zip_derived_cl336,zip_derived_cl331]) ).
thf(zip_derived_cl348_168,plain,
( '#form64'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl350,plain,
( ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58' ),
inference(renaming,[status(thm)],[zip_derived_cl341,zip_derived_cl348]) ).
thf(zip_derived_cl345_169,plain,
( '#form62'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl356,plain,
( ~ '#form62'
| ~ '#form58'
| ~ '#form56'
| ~ '#form52'
| ~ '#form48'
| ~ '#form44'
| ~ '#form40'
| ~ '#form36'
| ~ '#form30'
| ~ '#form23'
| ~ '#form17'
| ~ '#form13'
| ~ '#form9'
| ~ '#form5'
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) )
| ~ '#form7'
| ~ '#form11'
| ~ '#form15'
| ~ '#form21'
| ~ '#form27'
| ~ '#form33'
| ~ '#form38'
| ~ '#form42'
| ~ '#form46'
| ~ '#form50'
| ~ '#form54'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form60'
| ~ '#form64' ),
inference(renaming,[status(thm)],[zip_derived_cl350,zip_derived_cl345]) ).
thf(zip_derived_cl362_170,plain,
( '#form67'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl365,plain,
( ~ '#form67'
| ~ '#form64'
| ~ '#form60'
| ~ ( '#form19' @ pv5 @ '#sk2' )
| ~ '#form54'
| ~ '#form50'
| ~ '#form46'
| ~ '#form42'
| ~ '#form38'
| ~ '#form33'
| ~ '#form27'
| ~ '#form21'
| ~ '#form15'
| ~ '#form11'
| ~ '#form7'
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form5'
| ~ '#form9'
| ~ '#form13'
| ~ '#form17'
| ~ '#form23'
| ~ '#form30'
| ~ '#form36'
| ~ '#form40'
| ~ '#form44'
| ~ '#form48'
| ~ '#form52'
| ~ '#form56'
| ~ '#form58'
| ~ '#form62' ),
inference(renaming,[status(thm)],[zip_derived_cl356,zip_derived_cl362]) ).
thf(zip_derived_cl554_171,plain,
'#form67',
inference(clc,[status(thm)],[zip_derived_cl550,zip_derived_cl371]) ).
thf(zip_derived_cl482_172,plain,
'#form19' @ pv5 @ '#sk2',
inference(simplify,[status(thm)],[zip_derived_cl477]) ).
thf(zip_derived_cl559_173,plain,
'#form54',
inference(clc,[status(thm)],[zip_derived_cl555,zip_derived_cl318]) ).
thf(zip_derived_cl564_174,plain,
'#form50',
inference(clc,[status(thm)],[zip_derived_cl560,zip_derived_cl304]) ).
thf(zip_derived_cl577_175,plain,
'#form46',
inference(clc,[status(thm)],[zip_derived_cl565,zip_derived_cl290]) ).
thf(zip_derived_cl582_176,plain,
'#form42',
inference(clc,[status(thm)],[zip_derived_cl578,zip_derived_cl276]) ).
thf(zip_derived_cl587_177,plain,
'#form38',
inference(clc,[status(thm)],[zip_derived_cl583,zip_derived_cl262]) ).
thf(zip_derived_cl592_178,plain,
'#form33',
inference(clc,[status(thm)],[zip_derived_cl588,zip_derived_cl236]) ).
thf(zip_derived_cl597_179,plain,
'#form27',
inference(clc,[status(thm)],[zip_derived_cl593,zip_derived_cl209]) ).
thf(zip_derived_cl624_180,plain,
'#form21',
inference(clc,[status(thm)],[zip_derived_cl620,zip_derived_cl185]) ).
thf(zip_derived_cl629_181,plain,
'#form15',
inference(clc,[status(thm)],[zip_derived_cl625,zip_derived_cl161]) ).
thf(zip_derived_cl602_182,plain,
'#form11',
inference(clc,[status(thm)],[zip_derived_cl598,zip_derived_cl143]) ).
thf(zip_derived_cl619_183,plain,
'#form7',
inference(clc,[status(thm)],[zip_derived_cl615,zip_derived_cl125]) ).
thf(zip_derived_cl440_184,plain,
'#form5',
inference(clc,[status(thm)],[zip_derived_cl436,zip_derived_cl120]) ).
thf(zip_derived_cl445_185,plain,
'#form9',
inference(clc,[status(thm)],[zip_derived_cl441,zip_derived_cl138]) ).
thf(zip_derived_cl450_186,plain,
'#form13',
inference(clc,[status(thm)],[zip_derived_cl446,zip_derived_cl156]) ).
thf(zip_derived_cl459_187,plain,
'#form17',
inference(clc,[status(thm)],[zip_derived_cl455,zip_derived_cl177]) ).
thf(zip_derived_cl464_188,plain,
'#form23',
inference(clc,[status(thm)],[zip_derived_cl460,zip_derived_cl201]) ).
thf(zip_derived_cl498_189,plain,
'#form30',
inference(clc,[status(thm)],[zip_derived_cl470,zip_derived_cl224]) ).
thf(zip_derived_cl469_190,plain,
'#form36',
inference(clc,[status(thm)],[zip_derived_cl465,zip_derived_cl253]) ).
thf(zip_derived_cl519_191,plain,
'#form40',
inference(clc,[status(thm)],[zip_derived_cl515,zip_derived_cl273]) ).
thf(zip_derived_cl524_192,plain,
'#form44',
inference(clc,[status(thm)],[zip_derived_cl520,zip_derived_cl287]) ).
thf(zip_derived_cl529_193,plain,
'#form48',
inference(clc,[status(thm)],[zip_derived_cl525,zip_derived_cl301]) ).
thf(zip_derived_cl534_194,plain,
'#form52',
inference(clc,[status(thm)],[zip_derived_cl530,zip_derived_cl315]) ).
thf(zip_derived_cl539_195,plain,
'#form56',
inference(clc,[status(thm)],[zip_derived_cl535,zip_derived_cl327]) ).
thf(zip_derived_cl544_196,plain,
'#form58',
inference(clc,[status(thm)],[zip_derived_cl540,zip_derived_cl339]) ).
thf(zip_derived_cl549_197,plain,
'#form62',
inference(clc,[status(thm)],[zip_derived_cl545,zip_derived_cl354]) ).
thf(zip_derived_cl972,plain,
( ~ '#form64'
| ~ '#form60'
| ( rel_s4 @ '#sk2' @ '#sk3' )
| ( rel_s4 @ '#sk2' @ '#sk4' ) ),
inference(demod,[status(thm)],[zip_derived_cl365,zip_derived_cl554,zip_derived_cl482,zip_derived_cl559,zip_derived_cl564,zip_derived_cl577,zip_derived_cl582,zip_derived_cl587,zip_derived_cl592,zip_derived_cl597,zip_derived_cl624,zip_derived_cl629,zip_derived_cl602,zip_derived_cl619,zip_derived_cl440,zip_derived_cl445,zip_derived_cl450,zip_derived_cl459,zip_derived_cl464,zip_derived_cl498,zip_derived_cl469,zip_derived_cl519,zip_derived_cl524,zip_derived_cl529,zip_derived_cl534,zip_derived_cl539,zip_derived_cl544,zip_derived_cl549]) ).
thf(zip_derived_cl1036,plain,
( ~ '#form64'
| ~ '#form60'
| ( rel_s4 @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl1032,zip_derived_cl972]) ).
thf(zip_derived_cl1089,plain,
( ( rel_s4 @ '#sk2' @ '#sk4' )
| ~ '#form64'
| ~ '#form60' ),
inference(clc,[status(thm)],[zip_derived_cl1085,zip_derived_cl1036]) ).
thf(zip_derived_cl1108,plain,
( ~ '#form64'
| ~ '#form60'
| ~ ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl1106,zip_derived_cl1089]) ).
thf(zip_derived_cl1109,plain,
( ~ ( rel_s4 @ '#sk2' @ '#sk3' )
| ~ '#form60'
| ~ '#form64' ),
inference('sup-',[status(thm)],[zip_derived_cl99,zip_derived_cl1108]) ).
thf(zip_derived_cl1036_198,plain,
( ~ '#form64'
| ~ '#form60'
| ( rel_s4 @ '#sk2' @ '#sk3' ) ),
inference(clc,[status(thm)],[zip_derived_cl1032,zip_derived_cl972]) ).
thf(zip_derived_cl1111,plain,
( ~ '#form64'
| ~ '#form60' ),
inference(clc,[status(thm)],[zip_derived_cl1109,zip_derived_cl1036]) ).
thf(zip_derived_cl334_199,plain,
( '#form60'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ pv5 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl335,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk2' @ '#sk61' ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk61' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk61' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ pv5 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl334]) ).
thf(zip_derived_cl343,plain,
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk61' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk61' @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ pv5 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl335]) ).
thf(zip_derived_cl351,plain,
( ~ ( ( exists_in_world @ '#sk66' @ '#sk61' )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk61' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ '#sk66' @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ '#sk66' @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ pv5 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl343]) ).
thf(zip_derived_cl360,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk61' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ '#sk66' @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ '#sk66' @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ pv5 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl351]) ).
thf(zip_derived_cl367,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk61' @ '#sk70' ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk70' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk70' @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ '#sk66' @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ '#sk66' @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl360]) ).
thf(zip_derived_cl375,plain,
( ( rel_s4 @ '#sk61' @ '#sk70' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl367]) ).
thf(zip_derived_cl359,plain,
( ( exists_in_world @ '#sk66' @ '#sk61' )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl351]) ).
thf(zip_derived_cl342,plain,
( ( rel_s4 @ '#sk2' @ '#sk61' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl335]) ).
thf(zip_derived_cl376,plain,
( ~ ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ '#sk70' )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ '#sk70' @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ '#sk66' @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ '#sk66' @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ pv5 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl367]) ).
thf(zip_derived_cl378,plain,
( ~ ( ( exists_in_world @ '#sk72' @ '#sk70' )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk70' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk66' @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk66' @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk72' @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk72' @ Y1 ) ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl376]) ).
thf(zip_derived_cl381,plain,
( ( exists_in_world @ '#sk72' @ '#sk70' )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl378]) ).
thf(zip_derived_cl359_200,plain,
( ( exists_in_world @ '#sk66' @ '#sk61' )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl351]) ).
thf(zip_derived_cl375_201,plain,
( ( rel_s4 @ '#sk61' @ '#sk70' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl367]) ).
thf(zip_derived_cl342_202,plain,
( ( rel_s4 @ '#sk2' @ '#sk61' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl335]) ).
thf(zip_derived_cl382,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk70' @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk66' @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk66' @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ '#sk72' @ pv5 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ '#sk72' @ Y1 ) ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl378]) ).
thf(zip_derived_cl384,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk70' @ '#sk74' ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ n0 @ '#sk66' @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ '#sk66' @ n2 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ '#sk72' @ pv5 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ n0 @ '#sk72' @ Y0 ) ) ) ) )
| '#form60' ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl382]) ).
thf(zip_derived_cl387,plain,
( ( rel_s4 @ '#sk70' @ '#sk74' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl159_203,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl150]) ).
thf(zip_derived_cl169_204,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl171,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ X6 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl159,zip_derived_cl169]) ).
thf(zip_derived_cl169_205,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl181,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl171,zip_derived_cl169]) ).
thf(zip_derived_cl181_206,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl171,zip_derived_cl169]) ).
thf(zip_derived_cl193,plain,
! [X4: mu,X10: $i] :
( ( '#form25' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl195,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ pv5 @ Y0 ) ) )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl181,zip_derived_cl193]) ).
thf(zip_derived_cl205,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X10 @ ( '#sk29' @ X8 @ X10 ) ) )
| ( leq @ X8 @ pv5 @ ( '#sk29' @ X8 @ X10 ) ) )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl195]) ).
thf(zip_derived_cl217,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk29' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl217_207,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk29' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl230,plain,
! [X4: mu,X8: mu,X10: $i] :
( ( '#form35' @ X4 @ X8 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl233,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form35' @ X4 @ X8 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ( rel_s4 @ X10 @ ( '#sk29' @ X8 @ X10 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl217,zip_derived_cl230]) ).
thf(zip_derived_cl683,plain,
! [X0: mu,X1: mu,X2: $i] :
( '#form60'
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| ~ ( '#form25' @ X1 @ '#sk74' )
| ~ ( '#form19' @ X1 @ '#sk74' )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X1 @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk70' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form35' @ X1 @ X0 @ '#sk74' ) ),
inference('sup-',[status(thm)],[zip_derived_cl387,zip_derived_cl233]) ).
thf(zip_derived_cl1253,plain,
! [X0: mu,X1: mu] :
( '#form60'
| ~ ( '#form35' @ X1 @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( rel_s4 @ '#sk61' @ '#sk70' )
| ~ ( exists_in_world @ X1 @ '#sk61' )
| ~ ( '#form19' @ X1 @ '#sk74' )
| ~ ( '#form25' @ X1 @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| '#form60' ),
inference('sup-',[status(thm)],[zip_derived_cl342,zip_derived_cl683]) ).
thf(zip_derived_cl1260,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| ~ ( '#form25' @ X1 @ '#sk74' )
| ~ ( '#form19' @ X1 @ '#sk74' )
| ~ ( exists_in_world @ X1 @ '#sk61' )
| ~ ( rel_s4 @ '#sk61' @ '#sk70' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form35' @ X1 @ X0 @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1253]) ).
thf(zip_derived_cl1262,plain,
! [X0: mu,X1: mu] :
( '#form60'
| '#form60'
| ~ ( '#form35' @ X1 @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( exists_in_world @ X1 @ '#sk61' )
| ~ ( '#form19' @ X1 @ '#sk74' )
| ~ ( '#form25' @ X1 @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl375,zip_derived_cl1260]) ).
thf(zip_derived_cl1264,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| ~ ( '#form25' @ X1 @ '#sk74' )
| ~ ( '#form19' @ X1 @ '#sk74' )
| ~ ( exists_in_world @ X1 @ '#sk61' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form35' @ X1 @ X0 @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1262]) ).
thf(zip_derived_cl1280,plain,
! [X0: mu] :
( '#form60'
| '#form60'
| ~ ( '#form35' @ '#sk66' @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ~ ( '#form25' @ '#sk66' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl359,zip_derived_cl1264]) ).
thf(zip_derived_cl1282,plain,
! [X0: mu] :
( ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| ~ ( '#form25' @ '#sk66' @ '#sk74' )
| ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form35' @ '#sk66' @ X0 @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1280]) ).
thf(zip_derived_cl193_208,plain,
! [X4: mu,X10: $i] :
( ( '#form25' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl194,plain,
! [X4: mu,X10: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X10 @ ( '#sk26' @ X4 @ X10 ) ) )
| ( leq @ X4 @ n2 @ ( '#sk26' @ X4 @ X10 ) ) )
| ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl193]) ).
thf(zip_derived_cl207,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ X4 @ n2 @ ( '#sk26' @ X4 @ X10 ) )
| ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl194]) ).
thf(zip_derived_cl206,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk26' @ X4 @ X10 ) )
| ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl194]) ).
thf(zip_derived_cl390,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ '#sk66' @ n2 @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl396,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ X2 ) )
| ( leq @ '#sk66' @ n2 @ X2 )
| '#form60' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl390]) ).
thf(zip_derived_cl407,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk74' @ X2 )
| ( leq @ '#sk66' @ n2 @ X2 )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl396]) ).
thf(zip_derived_cl486,plain,
! [X0: mu] :
( ( '#form25' @ X0 @ '#sk74' )
| '#form60'
| ( leq @ '#sk66' @ n2 @ ( '#sk26' @ X0 @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl206,zip_derived_cl407]) ).
thf(zip_derived_cl570,plain,
( ( '#form25' @ '#sk66' @ '#sk74' )
| '#form60'
| ( '#form25' @ '#sk66' @ '#sk74' ) ),
inference('sup+',[status(thm)],[zip_derived_cl207,zip_derived_cl486]) ).
thf(zip_derived_cl573,plain,
( '#form60'
| ( '#form25' @ '#sk66' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl570]) ).
thf(zip_derived_cl1284,plain,
! [X0: mu] :
( '#form60'
| ~ ( '#form35' @ '#sk66' @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1282,zip_derived_cl573]) ).
thf(zip_derived_cl183_209,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl182_210,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl389,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ n0 @ '#sk66' @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl395,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ X2 ) )
| ( leq @ n0 @ '#sk66' @ X2 )
| '#form60' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl389]) ).
thf(zip_derived_cl406,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk74' @ X2 )
| ( leq @ n0 @ '#sk66' @ X2 )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl395]) ).
thf(zip_derived_cl475,plain,
! [X0: mu] :
( ( '#form19' @ X0 @ '#sk74' )
| '#form60'
| ( leq @ n0 @ '#sk66' @ ( '#sk20' @ X0 @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl182,zip_derived_cl406]) ).
thf(zip_derived_cl491,plain,
( ( '#form19' @ '#sk66' @ '#sk74' )
| '#form60'
| ( '#form19' @ '#sk66' @ '#sk74' ) ),
inference('sup+',[status(thm)],[zip_derived_cl183,zip_derived_cl475]) ).
thf(zip_derived_cl494,plain,
( '#form60'
| ( '#form19' @ '#sk66' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl491]) ).
thf(zip_derived_cl1285,plain,
! [X0: mu] :
( ( rel_s4 @ '#sk74' @ ( '#sk29' @ X0 @ '#sk74' ) )
| ~ ( exists_in_world @ X0 @ '#sk70' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form35' @ '#sk66' @ X0 @ '#sk74' )
| '#form60' ),
inference(clc,[status(thm)],[zip_derived_cl1284,zip_derived_cl494]) ).
thf(zip_derived_cl1286,plain,
( '#form60'
| '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ '#sk72' @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl381,zip_derived_cl1285]) ).
thf(zip_derived_cl1288,plain,
( ( rel_s4 @ '#sk74' @ ( '#sk29' @ '#sk72' @ '#sk74' ) )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1286]) ).
thf(zip_derived_cl183_211,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl182_212,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl392,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ n0 @ '#sk72' @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl398,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ X2 ) )
| ( leq @ n0 @ '#sk72' @ X2 )
| '#form60' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl392]) ).
thf(zip_derived_cl409,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk74' @ X2 )
| ( leq @ n0 @ '#sk72' @ X2 )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl398]) ).
thf(zip_derived_cl633,plain,
! [X0: mu] :
( ( '#form19' @ X0 @ '#sk74' )
| '#form60'
| ( leq @ n0 @ '#sk72' @ ( '#sk20' @ X0 @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl182,zip_derived_cl409]) ).
thf(zip_derived_cl781,plain,
( ( '#form19' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form19' @ '#sk72' @ '#sk74' ) ),
inference('sup+',[status(thm)],[zip_derived_cl183,zip_derived_cl633]) ).
thf(zip_derived_cl784,plain,
( '#form60'
| ( '#form19' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl781]) ).
thf(zip_derived_cl1290,plain,
( '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ ( '#sk29' @ '#sk72' @ '#sk74' ) ) ),
inference(clc,[status(thm)],[zip_derived_cl1288,zip_derived_cl784]) ).
thf(zip_derived_cl391,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( leq @ '#sk72' @ pv5 @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl397,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ X2 ) )
| ( leq @ '#sk72' @ pv5 @ X2 )
| '#form60' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl391]) ).
thf(zip_derived_cl408,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk74' @ X2 )
| ( leq @ '#sk72' @ pv5 @ X2 )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl397]) ).
thf(zip_derived_cl1292,plain,
( ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| '#form60'
| ( leq @ '#sk72' @ pv5 @ ( '#sk29' @ '#sk72' @ '#sk74' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl1290,zip_derived_cl408]) ).
thf(zip_derived_cl1310,plain,
( ( leq @ '#sk72' @ pv5 @ ( '#sk29' @ '#sk72' @ '#sk74' ) )
| '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1292]) ).
thf(zip_derived_cl218,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( leq @ X8 @ pv5 @ ( '#sk29' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl205]) ).
thf(zip_derived_cl230_213,plain,
! [X4: mu,X8: mu,X10: $i] :
( ( '#form35' @ X4 @ X8 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl234,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form35' @ X4 @ X8 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( leq @ X8 @ pv5 @ ( '#sk29' @ X8 @ X10 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl218,zip_derived_cl230]) ).
thf(zip_derived_cl1317,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ~ ( '#form25' @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ '#sk72' @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( '#form35' @ X0 @ '#sk72' @ '#sk74' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1310,zip_derived_cl234]) ).
thf(zip_derived_cl1415,plain,
! [X0: mu,X1: $i] :
( '#form60'
| ~ ( '#form35' @ X0 @ '#sk72' @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( rel_s4 @ X1 @ '#sk74' )
| ~ ( exists_in_world @ '#sk72' @ X1 )
| ~ ( rel_s4 @ '#sk61' @ X1 )
| ~ ( exists_in_world @ X0 @ '#sk61' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( '#form25' @ X0 @ '#sk74' )
| '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference('sup-',[status(thm)],[zip_derived_cl342,zip_derived_cl1317]) ).
thf(zip_derived_cl1426,plain,
! [X0: mu,X1: $i] :
( ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ~ ( '#form25' @ X0 @ '#sk74' )
| ~ ( '#form19' @ X0 @ '#sk74' )
| ~ ( exists_in_world @ X0 @ '#sk61' )
| ~ ( rel_s4 @ '#sk61' @ X1 )
| ~ ( exists_in_world @ '#sk72' @ X1 )
| ~ ( rel_s4 @ X1 @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( '#form35' @ X0 @ '#sk72' @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1415]) ).
thf(zip_derived_cl1428,plain,
! [X0: $i] :
( '#form60'
| '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ '#sk61' @ X0 )
| ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ~ ( '#form25' @ '#sk66' @ '#sk74' )
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference('sup-',[status(thm)],[zip_derived_cl359,zip_derived_cl1426]) ).
thf(zip_derived_cl1430,plain,
! [X0: $i] :
( ~ ( '#form25' @ '#sk66' @ '#sk74' )
| ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ~ ( rel_s4 @ '#sk61' @ X0 )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1428]) ).
thf(zip_derived_cl573_214,plain,
( '#form60'
| ( '#form25' @ '#sk66' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl570]) ).
thf(zip_derived_cl1432,plain,
! [X0: $i] :
( '#form60'
| ~ ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ '#sk61' @ X0 )
| ~ ( '#form19' @ '#sk66' @ '#sk74' ) ),
inference(clc,[status(thm)],[zip_derived_cl1430,zip_derived_cl573]) ).
thf(zip_derived_cl388,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl394,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl388]) ).
thf(zip_derived_cl405,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk74' @ '#sk76' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' ) )
| '#form60'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl394]) ).
thf(zip_derived_cl415,plain,
( ( rel_s4 @ '#sk74' @ '#sk76' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl405]) ).
thf(zip_derived_cl422,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk74' @ '#sk78' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk78' ) )
| '#form60'
| ( rel_s4 @ '#sk74' @ '#sk76' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl415]) ).
thf(zip_derived_cl426,plain,
( ( rel_s4 @ '#sk74' @ '#sk78' )
| ( rel_s4 @ '#sk74' @ '#sk76' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl422]) ).
thf(zip_derived_cl230_215,plain,
! [X4: mu,X8: mu,X10: $i] :
( ( '#form35' @ X4 @ X8 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl232,plain,
! [X4: mu,X8: mu,X10: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl230]) ).
thf(zip_derived_cl247,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl232]) ).
thf(zip_derived_cl260,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl247]) ).
thf(zip_derived_cl746,plain,
! [X0: mu,X1: mu] :
( '#form60'
| ( rel_s4 @ '#sk74' @ '#sk76' )
| ( '#form35' @ X1 @ X0 @ '#sk74' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ X0 ) @ use @ '#sk78' ) ),
inference('sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl260]) ).
thf(zip_derived_cl427,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk78' )
| ( rel_s4 @ '#sk74' @ '#sk76' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl422]) ).
thf(zip_derived_cl1205,plain,
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ '#sk76' )
| '#form60'
| '#form60'
| ( rel_s4 @ '#sk74' @ '#sk76' ) ),
inference('sup-',[status(thm)],[zip_derived_cl746,zip_derived_cl427]) ).
thf(zip_derived_cl1212,plain,
( '#form60'
| ( rel_s4 @ '#sk74' @ '#sk76' )
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1205]) ).
thf(zip_derived_cl231,plain,
! [X4: mu,X8: mu,X10: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl230]) ).
thf(zip_derived_cl246,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl231]) ).
thf(zip_derived_cl259,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl246]) ).
thf(zip_derived_cl1221,plain,
! [X0: mu,X1: mu] :
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form35' @ X1 @ X0 @ '#sk74' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ X0 ) @ use @ '#sk76' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1212,zip_derived_cl259]) ).
thf(zip_derived_cl416,plain,
( ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk74' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ Y0 ) ) )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl405]) ).
thf(zip_derived_cl423,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk74' @ '#sk78' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk78' ) )
| '#form60'
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl416]) ).
thf(zip_derived_cl429,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk78' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl423]) ).
thf(zip_derived_cl426_216,plain,
( ( rel_s4 @ '#sk74' @ '#sk78' )
| ( rel_s4 @ '#sk74' @ '#sk76' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl422]) ).
thf(zip_derived_cl259_217,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl246]) ).
thf(zip_derived_cl721,plain,
! [X0: mu,X1: mu] :
( '#form60'
| ( rel_s4 @ '#sk74' @ '#sk78' )
| ( '#form35' @ X1 @ X0 @ '#sk74' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ X0 ) @ use @ '#sk76' ) ),
inference('sup-',[status(thm)],[zip_derived_cl426,zip_derived_cl259]) ).
thf(zip_derived_cl428,plain,
( ( rel_s4 @ '#sk74' @ '#sk78' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl423]) ).
thf(zip_derived_cl1112,plain,
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ( rel_s4 @ '#sk74' @ '#sk78' )
| '#form60'
| '#form60'
| ( rel_s4 @ '#sk74' @ '#sk78' ) ),
inference('sup-',[status(thm)],[zip_derived_cl721,zip_derived_cl428]) ).
thf(zip_derived_cl1114,plain,
( '#form60'
| ( rel_s4 @ '#sk74' @ '#sk78' )
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1112]) ).
thf(zip_derived_cl260_218,plain,
! [X4: mu,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ( '#form35' @ X4 @ X8 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl247]) ).
thf(zip_derived_cl1120,plain,
! [X0: mu,X1: mu] :
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form35' @ X1 @ X0 @ '#sk74' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ X0 ) @ use @ '#sk78' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1114,zip_derived_cl260]) ).
thf(zip_derived_cl1360,plain,
( '#form60'
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' )
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference('sup+',[status(thm)],[zip_derived_cl429,zip_derived_cl1120]) ).
thf(zip_derived_cl1364,plain,
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk66' @ '#sk72' ) @ use @ '#sk76' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1360]) ).
thf(zip_derived_cl1394,plain,
( ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' )
| '#form60'
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1221,zip_derived_cl1364]) ).
thf(zip_derived_cl1398,plain,
( '#form60'
| ( '#form35' @ '#sk66' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl1394]) ).
thf(zip_derived_cl1433,plain,
! [X0: $i] :
( ~ ( '#form19' @ '#sk66' @ '#sk74' )
| ~ ( rel_s4 @ '#sk61' @ X0 )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| '#form60' ),
inference(clc,[status(thm)],[zip_derived_cl1432,zip_derived_cl1398]) ).
thf(zip_derived_cl494_219,plain,
( '#form60'
| ( '#form19' @ '#sk66' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl491]) ).
thf(zip_derived_cl1434,plain,
! [X0: $i] :
( '#form60'
| ~ ( '#form19' @ '#sk72' @ '#sk74' )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ '#sk61' @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl1433,zip_derived_cl494]) ).
thf(zip_derived_cl784_220,plain,
( '#form60'
| ( '#form19' @ '#sk72' @ '#sk74' ) ),
inference(simplify,[status(thm)],[zip_derived_cl781]) ).
thf(zip_derived_cl1435,plain,
! [X0: $i] :
( ~ ( rel_s4 @ '#sk61' @ X0 )
| ~ ( exists_in_world @ '#sk72' @ X0 )
| ~ ( rel_s4 @ X0 @ '#sk74' )
| '#form60' ),
inference(clc,[status(thm)],[zip_derived_cl1434,zip_derived_cl784]) ).
thf(zip_derived_cl1436,plain,
( '#form60'
| '#form60'
| ~ ( rel_s4 @ '#sk70' @ '#sk74' )
| ~ ( exists_in_world @ '#sk72' @ '#sk70' ) ),
inference('sup-',[status(thm)],[zip_derived_cl375,zip_derived_cl1435]) ).
thf(zip_derived_cl1442,plain,
( ~ ( exists_in_world @ '#sk72' @ '#sk70' )
| ~ ( rel_s4 @ '#sk70' @ '#sk74' )
| '#form60' ),
inference(simplify,[status(thm)],[zip_derived_cl1436]) ).
thf(zip_derived_cl381_221,plain,
( ( exists_in_world @ '#sk72' @ '#sk70' )
| '#form60' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl378]) ).
thf(zip_derived_cl1444,plain,
( '#form60'
| ~ ( rel_s4 @ '#sk70' @ '#sk74' ) ),
inference(clc,[status(thm)],[zip_derived_cl1442,zip_derived_cl381]) ).
thf(zip_derived_cl387_222,plain,
( ( rel_s4 @ '#sk70' @ '#sk74' )
| '#form60' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl384]) ).
thf(zip_derived_cl1445,plain,
'#form60',
inference(clc,[status(thm)],[zip_derived_cl1444,zip_derived_cl387]) ).
thf(zip_derived_cl1446,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1451,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl357,plain,
( ( rel_s4 @ '#sk2' @ '#sk65' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl349]) ).
thf(zip_derived_cl1446_223,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1447,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl373,plain,
( ( exists_in_world @ '#sk69' @ '#sk65' )
| '#form64' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl366]) ).
thf(zip_derived_cl1446_224,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1448,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_225,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_226,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_227,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_228,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_229,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl400,plain,
( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl410,plain,
( ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl400]) ).
thf(zip_derived_cl417,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk75' @ '#sk77' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) )
| '#form64'
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl410]) ).
thf(zip_derived_cl424,plain,
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl417]) ).
thf(zip_derived_cl430,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk75' @ '#sk79' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) )
| '#form64'
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl424]) ).
thf(zip_derived_cl432,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl430]) ).
thf(zip_derived_cl1446_230,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1456,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl432,zip_derived_cl1446]) ).
thf(zip_derived_cl385,plain,
( ( exists_in_world @ '#sk73' @ '#sk71' )
| '#form64' ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl383]) ).
thf(zip_derived_cl1446_231,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1450,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_232,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_233,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_234,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl1456_235,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl432,zip_derived_cl1446]) ).
thf(zip_derived_cl20,plain,
( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( !!
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y4 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y1 @ Y3 ) @ use @ Y5 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y1 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y1 @ n2 @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ Y3 @ ( minus @ pv5 @ n1 ) @ Y5 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y5: $i] :
( ( (~) @ ( rel_s4 @ Y4 @ Y5 ) )
| ( leq @ n0 @ Y3 @ Y5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl52,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk2' @ X2 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ ( minus @ pv5 @ n1 ) @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl84,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y1 ) )
| ( !!
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y3 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ Y0 @ Y2 ) @ use @ Y4 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y0 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y0 @ n2 @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ Y2 @ ( minus @ pv5 @ n1 ) @ Y4 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y4: $i] :
( ( (~) @ ( rel_s4 @ Y3 @ Y4 ) )
| ( leq @ n0 @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl102,plain,
! [X2: $i,X4: mu] :
( ( ( exists_in_world @ X4 @ X2 )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ X4 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ X4 @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ ( minus @ pv5 @ n1 ) @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl84]) ).
thf(zip_derived_cl106,plain,
! [X2: $i,X4: mu] :
( ~ ( exists_in_world @ X4 @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X2 @ Y0 ) )
| ( !!
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y2 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y1 ) @ use @ Y3 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ X4 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ X4 @ n2 @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ Y1 @ ( minus @ pv5 @ n1 ) @ Y3 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y3: $i] :
( ( (~) @ ( rel_s4 @ Y2 @ Y3 ) )
| ( leq @ n0 @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl102]) ).
thf(zip_derived_cl113,plain,
! [X2: $i,X4: mu,X6: $i] :
( ( (~) @ ( rel_s4 @ X2 @ X6 ) )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ X4 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ X4 @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ ( minus @ pv5 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl106]) ).
thf(zip_derived_cl122,plain,
! [X2: $i,X4: mu,X6: $i] :
( ~ ( rel_s4 @ X2 @ X6 )
| ( !!
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X6 )
=> ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y1 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ Y0 ) @ use @ Y2 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ X4 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ X4 @ n2 @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ Y0 @ ( minus @ pv5 @ n1 ) @ Y2 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y2: $i] :
( ( (~) @ ( rel_s4 @ Y1 @ Y2 ) )
| ( leq @ n0 @ Y0 @ Y2 ) ) ) ) ) ) ) )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl113]) ).
thf(zip_derived_cl131,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu] :
( ( ( exists_in_world @ X8 @ X6 )
=> ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X4 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X4 @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X8 @ Y1 ) ) ) ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl122]) ).
thf(zip_derived_cl140,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu] :
( ~ ( exists_in_world @ X8 @ X6 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X6 @ Y0 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y1 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X4 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X4 @ n2 @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y1 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y1: $i] :
( ( (~) @ ( rel_s4 @ Y0 @ Y1 ) )
| ( leq @ n0 @ X8 @ Y1 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl131]) ).
thf(zip_derived_cl149,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( (~) @ ( rel_s4 @ X6 @ X10 ) )
| ( (~)
@ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl140]) ).
thf(zip_derived_cl158,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( rel_s4 @ X6 @ X10 )
| ~ ( ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) )
| ( (~)
@ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl149]) ).
thf(zip_derived_cl167,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( rel_s4 @ X6 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl169_236,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl179,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl167,zip_derived_cl169]) ).
thf(zip_derived_cl169_237,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl191,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X4 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl179,zip_derived_cl169]) ).
thf(zip_derived_cl193_238,plain,
! [X4: mu,X10: $i] :
( ( '#form25' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl203,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl191,zip_derived_cl193]) ).
thf(zip_derived_cl215,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) ) )
| ~ ( '#form19' @ X4 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl203]) ).
thf(zip_derived_cl226,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl242,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl226]) ).
thf(zip_derived_cl255,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl242]) ).
thf(zip_derived_cl1555,plain,
! [X0: mu,X1: $i,X2: $i,X3: mu] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ X3 @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form19' @ X3 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X3 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X3 ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1456,zip_derived_cl255]) ).
thf(zip_derived_cl2107,plain,
! [X0: mu,X1: mu,X2: $i] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ X2 )
| ~ ( rel_s4 @ '#sk65' @ X2 )
| ~ ( exists_in_world @ X1 @ '#sk65' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl1555]) ).
thf(zip_derived_cl2113,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X1 ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2107]) ).
thf(zip_derived_cl379,plain,
( ( rel_s4 @ '#sk65' @ '#sk71' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl377]) ).
thf(zip_derived_cl1446_239,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1449,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl2115,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X1 ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2113,zip_derived_cl1449]) ).
thf(zip_derived_cl2117,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2115]) ).
thf(zip_derived_cl207_240,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ X4 @ n2 @ ( '#sk26' @ X4 @ X10 ) )
| ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl194]) ).
thf(zip_derived_cl206_241,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk26' @ X4 @ X10 ) )
| ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl194]) ).
thf(zip_derived_cl402,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ '#sk69' @ n2 @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl412,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ X2 ) )
| ( leq @ '#sk69' @ n2 @ X2 )
| '#form64' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl402]) ).
thf(zip_derived_cl419,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ '#sk69' @ n2 @ X2 )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl412]) ).
thf(zip_derived_cl656,plain,
! [X0: mu] :
( ( '#form25' @ X0 @ '#sk75' )
| '#form64'
| ( leq @ '#sk69' @ n2 @ ( '#sk26' @ X0 @ '#sk75' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl206,zip_derived_cl419]) ).
thf(zip_derived_cl871,plain,
( ( '#form25' @ '#sk69' @ '#sk75' )
| '#form64'
| ( '#form25' @ '#sk69' @ '#sk75' ) ),
inference('sup+',[status(thm)],[zip_derived_cl207,zip_derived_cl656]) ).
thf(zip_derived_cl874,plain,
( '#form64'
| ( '#form25' @ '#sk69' @ '#sk75' ) ),
inference(simplify,[status(thm)],[zip_derived_cl871]) ).
thf(zip_derived_cl1446_242,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1494,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl183_243,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl182_244,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl401,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ n0 @ '#sk69' @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl411,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ X2 ) )
| ( leq @ n0 @ '#sk69' @ X2 )
| '#form64' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl401]) ).
thf(zip_derived_cl418,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ n0 @ '#sk69' @ X2 )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl411]) ).
thf(zip_derived_cl645,plain,
! [X0: mu] :
( ( '#form19' @ X0 @ '#sk75' )
| '#form64'
| ( leq @ n0 @ '#sk69' @ ( '#sk20' @ X0 @ '#sk75' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl182,zip_derived_cl418]) ).
thf(zip_derived_cl863,plain,
( ( '#form19' @ '#sk69' @ '#sk75' )
| '#form64'
| ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference('sup+',[status(thm)],[zip_derived_cl183,zip_derived_cl645]) ).
thf(zip_derived_cl866,plain,
( '#form64'
| ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference(simplify,[status(thm)],[zip_derived_cl863]) ).
thf(zip_derived_cl1446_245,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1493,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2119,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2117,zip_derived_cl1494,zip_derived_cl1493]) ).
thf(zip_derived_cl2121,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl2119]) ).
thf(zip_derived_cl183_246,plain,
! [X4: mu,X10: $i] :
( ~ ( leq @ n0 @ X4 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl182_247,plain,
! [X4: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk20' @ X4 @ X10 ) )
| ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl170]) ).
thf(zip_derived_cl404,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ n0 @ '#sk73' @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl414,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ X2 ) )
| ( leq @ n0 @ '#sk73' @ X2 )
| '#form64' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl404]) ).
thf(zip_derived_cl421,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ n0 @ '#sk73' @ X2 )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl414]) ).
thf(zip_derived_cl669,plain,
! [X0: mu] :
( ( '#form19' @ X0 @ '#sk75' )
| '#form64'
| ( leq @ n0 @ '#sk73' @ ( '#sk20' @ X0 @ '#sk75' ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl182,zip_derived_cl421]) ).
thf(zip_derived_cl905,plain,
( ( '#form19' @ '#sk73' @ '#sk75' )
| '#form64'
| ( '#form19' @ '#sk73' @ '#sk75' ) ),
inference('sup+',[status(thm)],[zip_derived_cl183,zip_derived_cl669]) ).
thf(zip_derived_cl908,plain,
( '#form64'
| ( '#form19' @ '#sk73' @ '#sk75' ) ),
inference(simplify,[status(thm)],[zip_derived_cl905]) ).
thf(zip_derived_cl1446_248,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1495,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2123,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2121,zip_derived_cl1495]) ).
thf(zip_derived_cl425,plain,
( ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl417]) ).
thf(zip_derived_cl431,plain,
( ~ ( ( (~) @ ( rel_s4 @ '#sk75' @ '#sk79' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) )
| '#form64'
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl425]) ).
thf(zip_derived_cl434,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl431]) ).
thf(zip_derived_cl1446_249,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1458,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl434,zip_derived_cl1446]) ).
thf(zip_derived_cl2125,plain,
( ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference(clc,[status(thm)],[zip_derived_cl2123,zip_derived_cl1458]) ).
thf(zip_derived_cl403,plain,
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ Y0 ) )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl393]) ).
thf(zip_derived_cl413,plain,
! [X2: $i] :
( ( (~) @ ( rel_s4 @ '#sk75' @ X2 ) )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ X2 )
| '#form64' ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl403]) ).
thf(zip_derived_cl420,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ X2 )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl413]) ).
thf(zip_derived_cl1446_250,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1454,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl420,zip_derived_cl1446]) ).
thf(zip_derived_cl227,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl215]) ).
thf(zip_derived_cl243,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl227]) ).
thf(zip_derived_cl256,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl243]) ).
thf(zip_derived_cl1655,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ X0 ) )
| ~ ( '#form19' @ X1 @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X1 @ X2 )
| ~ ( rel_s4 @ X2 @ X3 )
| ~ ( exists_in_world @ '#sk73' @ X3 )
| ~ ( rel_s4 @ X3 @ X0 )
| ~ ( '#form19' @ '#sk73' @ X0 )
| ~ ( '#form25' @ X1 @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X4 )
| ~ ( rel_s4 @ X0 @ X4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1454,zip_derived_cl256]) ).
thf(zip_derived_cl2126,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2125,zip_derived_cl1655]) ).
thf(zip_derived_cl1495_251,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2148,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference(demod,[status(thm)],[zip_derived_cl2126,zip_derived_cl1495]) ).
thf(zip_derived_cl2199,plain,
! [X0: mu,X1: $i,X2: $i] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1456,zip_derived_cl2148]) ).
thf(zip_derived_cl2214,plain,
! [X0: mu,X1: $i,X2: $i] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference(simplify,[status(thm)],[zip_derived_cl2199]) ).
thf(zip_derived_cl2218,plain,
! [X0: mu,X1: $i] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ '#sk71' )
| ~ ( exists_in_world @ '#sk73' @ '#sk71' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2214]) ).
thf(zip_derived_cl1450_252,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl2220,plain,
! [X0: mu,X1: $i] :
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ '#sk71' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2218,zip_derived_cl1450]) ).
thf(zip_derived_cl2222,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2220]) ).
thf(zip_derived_cl1449_253,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl2228,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2222,zip_derived_cl1449]) ).
thf(zip_derived_cl2230,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2228]) ).
thf(zip_derived_cl1493_254,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl1494_255,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl2232,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2230,zip_derived_cl1493,zip_derived_cl1494]) ).
thf(zip_derived_cl1458_256,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl434,zip_derived_cl1446]) ).
thf(zip_derived_cl2234,plain,
rel_s4 @ '#sk75' @ '#sk79',
inference(clc,[status(thm)],[zip_derived_cl2232,zip_derived_cl1458]) ).
thf(zip_derived_cl1450_257,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_258,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_259,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_260,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl1456_261,plain,
( ( rel_s4 @ '#sk75' @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl432,zip_derived_cl1446]) ).
thf(zip_derived_cl168,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X8 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( rel_s4 @ X6 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl158]) ).
thf(zip_derived_cl169_262,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl180,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl168,zip_derived_cl169]) ).
thf(zip_derived_cl169_263,plain,
! [X4: mu,X10: $i] :
( ( '#form19' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ n0 @ X4 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl192,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form19' @ X4 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl180,zip_derived_cl169]) ).
thf(zip_derived_cl193_264,plain,
! [X4: mu,X10: $i] :
( ( '#form25' @ X4 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X4 @ n2 @ Y0 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl204,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ Y0 ) ) )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(renaming,[status(thm)],[zip_derived_cl192,zip_derived_cl193]) ).
thf(zip_derived_cl216,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( ( (~) @ ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) ) )
| ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) ) )
| ~ ( '#form19' @ X4 @ X10 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl204]) ).
thf(zip_derived_cl228,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl244,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl228]) ).
thf(zip_derived_cl257,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl1559,plain,
! [X0: mu,X1: $i,X2: $i,X3: mu] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ X3 @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form19' @ X3 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X3 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X3 ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1456,zip_derived_cl257]) ).
thf(zip_derived_cl2153,plain,
! [X0: mu,X1: mu,X2: $i] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ X2 )
| ~ ( rel_s4 @ '#sk65' @ X2 )
| ~ ( exists_in_world @ X1 @ '#sk65' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl1559]) ).
thf(zip_derived_cl2159,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X1 ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2153]) ).
thf(zip_derived_cl1449_265,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl2161,plain,
! [X0: mu,X1: mu] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X1 ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2159,zip_derived_cl1449]) ).
thf(zip_derived_cl2163,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2161]) ).
thf(zip_derived_cl1494_266,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_267,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2165,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2163,zip_derived_cl1494,zip_derived_cl1493]) ).
thf(zip_derived_cl2167,plain,
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl2165]) ).
thf(zip_derived_cl1495_268,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2169,plain,
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2167,zip_derived_cl1495]) ).
thf(zip_derived_cl433,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl430]) ).
thf(zip_derived_cl1446_269,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1457,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl1446]) ).
thf(zip_derived_cl2171,plain,
( ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(clc,[status(thm)],[zip_derived_cl2169,zip_derived_cl1457]) ).
thf(zip_derived_cl1454_270,plain,
! [X2: $i] :
( ~ ( rel_s4 @ '#sk75' @ X2 )
| ( leq @ '#sk73' @ ( minus @ pv5 @ n1 ) @ X2 ) ),
inference(demod,[status(thm)],[zip_derived_cl420,zip_derived_cl1446]) ).
thf(zip_derived_cl229,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i] :
( ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ( !!
@ ^ [Y0: $i] :
( ( (~) @ ( rel_s4 @ X10 @ Y0 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ Y0 ) ) )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl216]) ).
thf(zip_derived_cl245,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ( (~) @ ( rel_s4 @ X10 @ X12 ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( '#form19' @ X4 @ X10 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl229]) ).
thf(zip_derived_cl258,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ~ ( leq @ X8 @ ( minus @ pv5 @ n1 ) @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl245]) ).
thf(zip_derived_cl1654,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ X0 ) )
| ~ ( '#form19' @ X1 @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X1 @ X2 )
| ~ ( rel_s4 @ X2 @ X3 )
| ~ ( exists_in_world @ '#sk73' @ X3 )
| ~ ( rel_s4 @ X3 @ X0 )
| ~ ( '#form19' @ '#sk73' @ X0 )
| ~ ( '#form25' @ X1 @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X4 )
| ~ ( rel_s4 @ X0 @ X4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1454,zip_derived_cl258]) ).
thf(zip_derived_cl2173,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2171,zip_derived_cl1654]) ).
thf(zip_derived_cl1495_271,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2195,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference(demod,[status(thm)],[zip_derived_cl2173,zip_derived_cl1495]) ).
thf(zip_derived_cl2332,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2234,zip_derived_cl2195]) ).
thf(zip_derived_cl2346,plain,
! [X0: mu,X1: $i] :
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X1 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X1 )
| ~ ( rel_s4 @ '#sk65' @ X1 )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form19' @ X0 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2332]) ).
thf(zip_derived_cl2352,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ '#sk73' @ '#sk71' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2346]) ).
thf(zip_derived_cl1449_272,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl1450_273,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl2354,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2352,zip_derived_cl1449,zip_derived_cl1450]) ).
thf(zip_derived_cl2356,plain,
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2354]) ).
thf(zip_derived_cl1494_274,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_275,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2358,plain,
( ( rel_s4 @ '#sk75' @ '#sk77' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2356,zip_derived_cl1494,zip_derived_cl1493]) ).
thf(zip_derived_cl1457_276,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl433,zip_derived_cl1446]) ).
thf(zip_derived_cl2360,plain,
rel_s4 @ '#sk75' @ '#sk77',
inference(clc,[status(thm)],[zip_derived_cl2358,zip_derived_cl1457]) ).
thf(zip_derived_cl1450_277,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_278,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_279,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_280,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl2360_281,plain,
rel_s4 @ '#sk75' @ '#sk77',
inference(clc,[status(thm)],[zip_derived_cl2358,zip_derived_cl1457]) ).
thf(zip_derived_cl255_282,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X8 ) @ use @ X12 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl242]) ).
thf(zip_derived_cl2368,plain,
! [X0: mu,X1: $i,X2: $i,X3: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ X3 @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form19' @ X3 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X3 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X3 ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2360,zip_derived_cl255]) ).
thf(zip_derived_cl2465,plain,
! [X0: mu,X1: mu,X2: $i] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ X2 )
| ~ ( rel_s4 @ '#sk65' @ X2 )
| ~ ( exists_in_world @ X1 @ '#sk65' )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2368]) ).
thf(zip_derived_cl2471,plain,
! [X0: mu,X1: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X1 ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2465]) ).
thf(zip_derived_cl1449_283,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl2473,plain,
! [X0: mu,X1: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ X1 ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2471,zip_derived_cl1449]) ).
thf(zip_derived_cl2475,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2473]) ).
thf(zip_derived_cl1494_284,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_285,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2477,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ X0 ) @ use @ '#sk77' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' ) ),
inference(demod,[status(thm)],[zip_derived_cl2475,zip_derived_cl1494,zip_derived_cl1493]) ).
thf(zip_derived_cl2479,plain,
( ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl2477]) ).
thf(zip_derived_cl1495_286,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2481,plain,
( ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2479,zip_derived_cl1495]) ).
thf(zip_derived_cl1450_287,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_288,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1451_289,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_290,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl2234_291,plain,
rel_s4 @ '#sk75' @ '#sk79',
inference(clc,[status(thm)],[zip_derived_cl2232,zip_derived_cl1458]) ).
thf(zip_derived_cl257_292,plain,
! [X2: $i,X4: mu,X6: $i,X8: mu,X10: $i,X12: $i] :
( ~ ( rel_s4 @ X10 @ X12 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X8 ) @ use @ X12 )
| ( rel_s4 @ X10 @ ( '#sk32' @ X8 @ X10 ) )
| ~ ( '#form25' @ X4 @ X10 )
| ~ ( '#form19' @ X8 @ X10 )
| ~ ( rel_s4 @ X6 @ X10 )
| ~ ( exists_in_world @ X8 @ X6 )
| ~ ( rel_s4 @ X2 @ X6 )
| ~ ( exists_in_world @ X4 @ X2 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( '#form19' @ X4 @ X10 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl244]) ).
thf(zip_derived_cl2241,plain,
! [X0: mu,X1: $i,X2: $i,X3: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ X3 @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form19' @ X3 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X3 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X3 ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2234,zip_derived_cl257]) ).
thf(zip_derived_cl2397,plain,
! [X0: mu,X1: mu,X2: $i] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ X2 )
| ~ ( rel_s4 @ '#sk65' @ X2 )
| ~ ( exists_in_world @ X1 @ '#sk65' )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2241]) ).
thf(zip_derived_cl2403,plain,
! [X0: mu,X1: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X1 ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2397]) ).
thf(zip_derived_cl1449_293,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl2405,plain,
! [X0: mu,X1: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( exists_in_world @ X1 @ '#sk71' )
| ~ ( '#form19' @ X1 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X1 @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ X1 ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2403,zip_derived_cl1449]) ).
thf(zip_derived_cl2407,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1448,zip_derived_cl2405]) ).
thf(zip_derived_cl1494_294,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_295,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2409,plain,
! [X0: mu] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ X0 ) @ use @ '#sk79' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ X0 @ '#sk75' ) )
| ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk71' ) ),
inference(demod,[status(thm)],[zip_derived_cl2407,zip_derived_cl1494,zip_derived_cl1493]) ).
thf(zip_derived_cl2411,plain,
( ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl2409]) ).
thf(zip_derived_cl1495_296,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2413,plain,
( ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2411,zip_derived_cl1495]) ).
thf(zip_derived_cl435,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' )
| '#form64' ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl431]) ).
thf(zip_derived_cl1446_297,plain,
~ '#form64',
inference(demod,[status(thm)],[zip_derived_cl1111,zip_derived_cl1445]) ).
thf(zip_derived_cl1459,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl435,zip_derived_cl1446]) ).
thf(zip_derived_cl2415,plain,
( ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ) )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2413,zip_derived_cl1459]) ).
thf(zip_derived_cl2483,plain,
rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ),
inference(clc,[status(thm)],[zip_derived_cl2481,zip_derived_cl2415]) ).
thf(zip_derived_cl1655_298,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ X0 ) )
| ~ ( '#form19' @ X1 @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X1 @ X2 )
| ~ ( rel_s4 @ X2 @ X3 )
| ~ ( exists_in_world @ '#sk73' @ X3 )
| ~ ( rel_s4 @ X3 @ X0 )
| ~ ( '#form19' @ '#sk73' @ X0 )
| ~ ( '#form25' @ X1 @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X4 )
| ~ ( rel_s4 @ X0 @ X4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1454,zip_derived_cl256]) ).
thf(zip_derived_cl2484,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2483,zip_derived_cl1655]) ).
thf(zip_derived_cl1495_299,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2506,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference(demod,[status(thm)],[zip_derived_cl2484,zip_derived_cl1495]) ).
thf(zip_derived_cl2512,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2360,zip_derived_cl2506]) ).
thf(zip_derived_cl2538,plain,
! [X0: mu,X1: $i] :
( ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X1 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X1 )
| ~ ( rel_s4 @ '#sk65' @ X1 )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form19' @ X0 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2512]) ).
thf(zip_derived_cl2544,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ '#sk73' @ '#sk71' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2538]) ).
thf(zip_derived_cl1449_300,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl1450_301,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl2546,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ z_defuse @ X0 @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl2544,zip_derived_cl1449,zip_derived_cl1450]) ).
thf(zip_derived_cl1451_302,plain,
rel_s4 @ '#sk71' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl399,zip_derived_cl1446]) ).
thf(zip_derived_cl1447_303,plain,
rel_s4 @ '#sk2' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl357,zip_derived_cl1446]) ).
thf(zip_derived_cl2234_304,plain,
rel_s4 @ '#sk75' @ '#sk79',
inference(clc,[status(thm)],[zip_derived_cl2232,zip_derived_cl1458]) ).
thf(zip_derived_cl2483_305,plain,
rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ '#sk75' ),
inference(clc,[status(thm)],[zip_derived_cl2481,zip_derived_cl2415]) ).
thf(zip_derived_cl1654_306,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i,X4: $i] :
( ~ ( rel_s4 @ '#sk75' @ ( '#sk32' @ '#sk73' @ X0 ) )
| ~ ( '#form19' @ X1 @ X0 )
| ~ ( rel_s4 @ '#sk2' @ X2 )
| ~ ( exists_in_world @ X1 @ X2 )
| ~ ( rel_s4 @ X2 @ X3 )
| ~ ( exists_in_world @ '#sk73' @ X3 )
| ~ ( rel_s4 @ X3 @ X0 )
| ~ ( '#form19' @ '#sk73' @ X0 )
| ~ ( '#form25' @ X1 @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X4 )
| ~ ( rel_s4 @ X0 @ X4 ) ),
inference('sup-',[status(thm)],[zip_derived_cl1454,zip_derived_cl258]) ).
thf(zip_derived_cl2485,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( '#form19' @ '#sk73' @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2483,zip_derived_cl1654]) ).
thf(zip_derived_cl1495_307,plain,
'#form19' @ '#sk73' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl908,zip_derived_cl1446]) ).
thf(zip_derived_cl2507,plain,
! [X0: $i,X1: mu,X2: $i,X3: $i] :
( ~ ( rel_s4 @ '#sk75' @ X0 )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X1 @ '#sk73' ) @ use @ X0 )
| ~ ( '#form25' @ X1 @ '#sk75' )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X3 @ X2 )
| ~ ( exists_in_world @ X1 @ X3 )
| ~ ( rel_s4 @ '#sk2' @ X3 )
| ~ ( '#form19' @ X1 @ '#sk75' ) ),
inference(demod,[status(thm)],[zip_derived_cl2485,zip_derived_cl1495]) ).
thf(zip_derived_cl2578,plain,
! [X0: mu,X1: $i,X2: $i] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ '#sk2' @ X1 )
| ~ ( exists_in_world @ X0 @ X1 )
| ~ ( rel_s4 @ X1 @ X2 )
| ~ ( exists_in_world @ '#sk73' @ X2 )
| ~ ( rel_s4 @ X2 @ '#sk75' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2234,zip_derived_cl2507]) ).
thf(zip_derived_cl2592,plain,
! [X0: mu,X1: $i] :
( ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ~ ( rel_s4 @ X1 @ '#sk75' )
| ~ ( exists_in_world @ '#sk73' @ X1 )
| ~ ( rel_s4 @ '#sk65' @ X1 )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form19' @ X0 @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1447,zip_derived_cl2578]) ).
thf(zip_derived_cl2598,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( rel_s4 @ '#sk65' @ '#sk71' )
| ~ ( exists_in_world @ '#sk73' @ '#sk71' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' ) ),
inference('sup-',[status(thm)],[zip_derived_cl1451,zip_derived_cl2592]) ).
thf(zip_derived_cl1449_308,plain,
rel_s4 @ '#sk65' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl379,zip_derived_cl1446]) ).
thf(zip_derived_cl1450_309,plain,
exists_in_world @ '#sk73' @ '#sk71',
inference(demod,[status(thm)],[zip_derived_cl385,zip_derived_cl1446]) ).
thf(zip_derived_cl2600,plain,
! [X0: mu] :
( ~ ( '#form19' @ X0 @ '#sk75' )
| ~ ( exists_in_world @ X0 @ '#sk65' )
| ~ ( '#form25' @ X0 @ '#sk75' )
| ( qmltpeq @ ( a_select3 @ u_defuse @ X0 @ '#sk73' ) @ use @ '#sk79' ) ),
inference(demod,[status(thm)],[zip_derived_cl2598,zip_derived_cl1449,zip_derived_cl1450]) ).
thf(zip_derived_cl1459_310,plain,
( ~ ( qmltpeq @ ( a_select3 @ u_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk79' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference(demod,[status(thm)],[zip_derived_cl435,zip_derived_cl1446]) ).
thf(zip_derived_cl2612,plain,
( ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( exists_in_world @ '#sk69' @ '#sk65' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' )
| ~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2600,zip_derived_cl1459]) ).
thf(zip_derived_cl1494_311,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_312,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_313,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2614,plain,
~ ( qmltpeq @ ( a_select3 @ z_defuse @ '#sk69' @ '#sk73' ) @ use @ '#sk77' ),
inference(demod,[status(thm)],[zip_derived_cl2612,zip_derived_cl1494,zip_derived_cl1448,zip_derived_cl1493]) ).
thf(zip_derived_cl2616,plain,
( ~ ( '#form25' @ '#sk69' @ '#sk75' )
| ~ ( exists_in_world @ '#sk69' @ '#sk65' )
| ~ ( '#form19' @ '#sk69' @ '#sk75' ) ),
inference('sup-',[status(thm)],[zip_derived_cl2546,zip_derived_cl2614]) ).
thf(zip_derived_cl1494_314,plain,
'#form25' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl874,zip_derived_cl1446]) ).
thf(zip_derived_cl1448_315,plain,
exists_in_world @ '#sk69' @ '#sk65',
inference(demod,[status(thm)],[zip_derived_cl373,zip_derived_cl1446]) ).
thf(zip_derived_cl1493_316,plain,
'#form19' @ '#sk69' @ '#sk75',
inference(demod,[status(thm)],[zip_derived_cl866,zip_derived_cl1446]) ).
thf(zip_derived_cl2620,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl2616,zip_derived_cl1494,zip_derived_cl1448,zip_derived_cl1493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV097^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TxONrwWHQW true
% 0.15/0.35 % Computer : n014.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Aug 29 04:31:30 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Running portfolio for 300 s
% 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36 % Number of cores: 8
% 0.15/0.36 % Python version: Python 3.6.8
% 0.15/0.36 % Running in HO mode
% 0.23/0.66 % Total configuration time : 828
% 0.23/0.66 % Estimated wc time : 1656
% 0.23/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.23/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.23/0.75 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.23/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.23/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.23/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 1.00/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 1.00/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 1.00/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 28.75/4.37 % Solved by lams/20_acsne_simpl.sh.
% 28.75/4.37 % done 1124 iterations in 2.804s
% 28.75/4.37 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 28.75/4.37 % SZS output start Refutation
% See solution above
% 29.19/4.46
% 29.19/4.46
% 29.19/4.46 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 29.19/4.46 % Terminating...
% 30.00/4.65 % Runner terminated.
% 30.00/4.65 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------