%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWV097^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : 600s
% DateTime : Wed Jul 20 21:23:40 EDT 2022
% Result : Theorem 48.29s 45.70s
% Output : Proof 48.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 45
% Syntax : Number of formulae : 51 ( 13 unt; 26 typ; 9 def)
% Number of atoms : 1434 ( 9 equ; 0 cnn)
% Maximal formula atoms : 186 ( 57 avg)
% Number of connectives : 6646 ( 746 ~; 5 |; 0 &;4506 @)
% ( 5 <=>;1383 =>; 0 <=; 0 <~>)
% Maximal formula depth : 126 ( 21 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 33 con; 0-3 aty)
% ( 1 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 791 ( 14 ^ 777 !; 0 ?; 791 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mu,type,
mu: $tType ).
thf(ty_n0,type,
n0: mu ).
thf(ty_n999,type,
n999: mu ).
thf(ty_rel_s4,type,
rel_s4: $i > $i > $o ).
thf(ty_eigen__2,type,
eigen__2: $i ).
thf(ty_xinit_defuse,type,
xinit_defuse: mu ).
thf(ty_z_defuse,type,
z_defuse: mu ).
thf(ty_a_select3,type,
a_select3: mu > mu > mu > mu ).
thf(ty_minus,type,
minus: mu > mu > mu ).
thf(ty_a_select2,type,
a_select2: mu > mu > mu ).
thf(ty_eigen__3,type,
eigen__3: $i ).
thf(ty_pv5,type,
pv5: mu ).
thf(ty_sigma_defuse,type,
sigma_defuse: mu ).
thf(ty_n1,type,
n1: mu ).
thf(ty_exists_in_world,type,
exists_in_world: mu > $i > $o ).
thf(ty_u_defuse,type,
u_defuse: mu ).
thf(ty_n2,type,
n2: mu ).
thf(ty_n5,type,
n5: mu ).
thf(ty_qmltpeq,type,
qmltpeq: mu > mu > $i > $o ).
thf(ty_use,type,
use: mu ).
thf(ty_leq,type,
leq: mu > mu > $i > $o ).
thf(ty_n3,type,
n3: mu ).
thf(ty_xinit_noise_defuse,type,
xinit_noise_defuse: mu ).
thf(ty_n4,type,
n4: mu ).
thf(ty_rho_defuse,type,
rho_defuse: mu ).
thf(ty_xinit_mean_defuse,type,
xinit_mean_defuse: mu ).
thf(h0,assumption,
! [X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__3,definition,
( eigen__3
= ( eps__0
@ ^ [X1: $i] :
~ ( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv5 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ pv5 @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ ( minus @ pv5 @ n1 ) @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv5 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ pv5 @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ ( minus @ pv5 @ n1 ) @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__3])]) ).
thf(eigendef_eigen__2,definition,
( eigen__2
= ( eps__0
@ ^ [X1: $i] :
~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__2])]) ).
thf(sP1,plain,
( sP1
<=> ( ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv5 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ pv5 @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ ( minus @ pv5 @ n1 ) @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv5 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ pv5 @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ ( minus @ pv5 @ n1 ) @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( rel_s4 @ eigen__2 @ eigen__3 )
=> sP1 ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ n0 @ pv5 @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X1 ) )
=> ( ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ pv5 @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) )
=> ~ ! [X1: $i] :
( ( rel_s4 @ eigen__3 @ X1 )
=> ! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ! [X3: $i] :
( ( rel_s4 @ X1 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ( ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X2 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ n0 @ X4 @ X6 ) )
=> ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X2 @ n2 @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( leq @ X4 @ ( minus @ pv5 @ n1 ) @ X6 ) ) ) ) )
=> ~ ( ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X2 @ X4 ) @ use @ X6 ) )
=> ~ ! [X6: $i] :
( ( rel_s4 @ X5 @ X6 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X2 @ X4 ) @ use @ X6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: $i] :
( ( rel_s4 @ eigen__2 @ X1 )
=> ( ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv5 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ pv5 @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ ( minus @ pv5 @ n1 ) @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ n0 @ pv5 @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X2 ) )
=> ( ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ pv5 @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) )
=> ~ ! [X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ! [X4: $i] :
( ( rel_s4 @ X2 @ X4 )
=> ! [X5: mu] :
( ( exists_in_world @ X5 @ X4 )
=> ! [X6: $i] :
( ( rel_s4 @ X4 @ X6 )
=> ( ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X3 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ n0 @ X5 @ X7 ) )
=> ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X3 @ n2 @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( leq @ X5 @ ( minus @ pv5 @ n1 ) @ X7 ) ) ) ) )
=> ~ ( ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X3 @ X5 ) @ use @ X7 ) )
=> ~ ! [X7: $i] :
( ( rel_s4 @ X6 @ X7 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X3 @ X5 ) @ use @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ( ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(def_mnot,definition,
( mnot
= ( ^ [X1: $i > $o,X2: $i] :
~ ( X1 @ X2 ) ) ) ).
thf(def_mor,definition,
( mor
= ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
( ~ ( X1 @ X3 )
=> ( X2 @ X3 ) ) ) ) ).
thf(def_mand,definition,
( mand
= ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mor @ ( mnot @ X1 ) @ ( mnot @ X2 ) ) ) ) ) ).
thf(def_mimplies,definition,
( mimplies
= ( ^ [X1: $i > $o] : ( mor @ ( mnot @ X1 ) ) ) ) ).
thf(def_mforall_ind,definition,
( mforall_ind
= ( ^ [X1: mu > $i > $o,X2: $i] :
! [X3: mu] :
( ( exists_in_world @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) ) ) ).
thf(def_mvalid,definition,
mvalid = !! ).
thf(def_mbox_s4,definition,
( mbox_s4
= ( ^ [X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ) ).
thf(quaternion_ds1_inuse_0009,conjecture,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(h1,negated_conjecture,
~ sP5,
inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0009]) ).
thf(1,plain,
( sP1
| sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( sP1
| ~ sP3 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( sP2
| ~ sP1 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( sP4
| ~ sP2 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).
thf(5,plain,
( sP5
| ~ sP4 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2]) ).
thf(6,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,h1]) ).
thf(7,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[6,h0]) ).
thf(0,theorem,
! [X1: $i,X2: $i] :
( ( rel_s4 @ X1 @ X2 )
=> ( ~ ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
=> ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ rho_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ sigma_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n0 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n1 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ n2 @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_mean_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n0 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n1 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n2 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n3 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n4 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( qmltpeq @ ( a_select2 @ xinit_noise_defuse @ n5 ) @ use @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ n0 @ pv5 @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ( leq @ pv5 @ ( minus @ n999 @ n1 ) @ X3 ) )
=> ~ ~ ( ~ ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ pv5 @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) )
=> ~ ! [X3: $i] :
( ( rel_s4 @ X2 @ X3 )
=> ! [X4: mu] :
( ( exists_in_world @ X4 @ X3 )
=> ! [X5: $i] :
( ( rel_s4 @ X3 @ X5 )
=> ! [X6: mu] :
( ( exists_in_world @ X6 @ X5 )
=> ! [X7: $i] :
( ( rel_s4 @ X5 @ X7 )
=> ( ~ ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X4 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ n0 @ X6 @ X8 ) )
=> ~ ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X4 @ n2 @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( leq @ X6 @ ( minus @ pv5 @ n1 ) @ X8 ) ) ) ) )
=> ~ ( ~ ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ u_defuse @ X4 @ X6 ) @ use @ X8 ) )
=> ~ ! [X8: $i] :
( ( rel_s4 @ X7 @ X8 )
=> ( qmltpeq @ ( a_select3 @ z_defuse @ X4 @ X6 ) @ use @ X8 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h1])],[6,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV097^7 : TPTP v8.1.0. Released v5.5.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 23:48:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 48.29/45.70 % SZS status Theorem
% 48.29/45.70 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 48.29/45.70 % Inferences: 169
% 48.29/45.70 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------